❤️ Quidditch 😂

"Quidditch is a fictional sport invented by author J.K. Rowling for her fantasy book series Harry Potter. It is a dangerous but popular sport played by witches and wizards riding flying broomsticks. Matches are played on a large oval pitch with three ring-shaped goals of different heights on each side, between two opposing teams of seven players each: three Chasers, two Beaters, the Keeper, and the Seeker. The Chasers and the Keeper respectively score with and defend the goals against the Quaffle; the two Beaters bat the Bludgers away from their teammates and towards their opponents; and the Seeker locates and catches the Golden Snitch, whose capture simultaneously wins the Seeker's team 150 points and ends the game. The team with the most points at the end wins. Harry Potter plays as Seeker for his house team at Hogwarts. Regional and international Quidditch competitions are mentioned throughout the series. Aspects of the sport's history are revealed in Quidditch Through the Ages, published by Rowling in 2001 to benefit Comic Relief. A real-life version of the game has been created, in which the players use brooms, but run instead of flying. Development Rowling came up with the sport in a Manchester hotel room after a row with her then-boyfriend. She explained: "I had been pondering the things that hold a society together, cause it to congregate and signify its particular character and knew I needed a sport." Rowling claims that the word "Quidditch" is not derived from any particular etymological root, but was the result of filling five pages of a notebook with different words beginning with "Q". Despite the sport's popularity with fans, Rowling grew to dislike describing the matches. She commented in an interview: The final Quidditch scene in the books appears in Harry Potter and the Half-Blood Prince. Rowling experienced "fiendish glee" writing this scene, which features memorable commentary by Luna Lovegood. In 2014 Rowling started publishing a series of match reports from the Quidditch World Cup on Pottermore, culminating in a short story about the final featuring the return of Harry, Ron, Hermione and their friends as adults. This generated interest from several media outlets, as it was the first new writing about the Harry Potter characters since the end of the series in 2007. Quidditch is introduced in Harry Potter and the Philosopher's Stone, and is a regularly recurring feature throughout the first six books. It is depicted as being played by both professionals (as in tournaments like the Quidditch World Cup) and amateurs. A major motif of five of the Harry Potter books is the competition among the four Hogwarts houses for the Quidditch Cup each school year; in particular, the rivalry between Gryffindor and Slytherin. Game progression The Golden Snitch Quidditch matches are played over an oval-shaped pitch, with a scoring area at each end consisting of three hooped goal posts, each at a different height. Each team is made up of seven players, consisting of three Chasers, two Beaters, one Keeper and one Seeker. The job of the Chasers is to keep possession of the scarlet Quaffle, a leather ball passed between players. They must attempt to score goals (worth 10 points) by throwing it through one of the opponents' three hoops. These hoops are defended by the opposing team's Keeper, who ideally tries to block their goals. Meanwhile, players of both teams are attacked indiscriminately by the two Bludgers. These are round, jet-black balls made of iron that fly around violently trying to knock players off their brooms. It is the Beaters' job to defend their teammates from the Bludgers; they carry short wooden clubs, which they use to knock the Bludgers away from their teammates and/or toward the opposing team. Finally, the role of the Seeker is to catch the Golden Snitch. This is a small golden ball the approximate size of a walnut. The winged Snitch is enchanted to hover, dart, and fly around the pitch, avoiding capture while remaining within the boundaries of the playing area. Catching the Snitch ends the game and scores the successful Seeker's team 150 points. As the team with the most points wins, this often guarantees victory for the successful Seeker's team. A notable exception is when Bulgaria Seeker Viktor Krum catches the Snitch for Bulgaria during the World Cup Final in Goblet of Fire, while his team are still 160 points behind Ireland (their opponents), thus making his own team lose by only 10 points. Broomsticks thumb Magical flying broomsticks are one of the forms of transportation for wizards and witches, as well as being used for playing Quidditch. The three most prominent broomsticks in the books are the Nimbus 2000, Nimbus 2001, and the Firebolt, both of which have been produced as merchandise by Warner Bros. The Nimbus is introduced as one of the best broomsticks in the wizarding world. Harry receives a Nimbus 2000 in Philosopher's Stone so that he can play for Gryffindor house. Lucius Malfoy buys a full set of the more advanced Nimbus 2001s for the Slytherin team as a bribe, so they would choose his son Draco as Seeker the following year. The Firebolt later supersedes the Nimbus as the fastest and one of the most expensive racing brooms in existence. Harry receives a Firebolt model from his godfather, Sirius Black, after his Nimbus 2000 is destroyed during a Quidditch match in Prisoner of Azkaban. In Goblet of Fire, Harry uses his Firebolt to escape the Hungarian Horntail (a dragon) during the Triwizard Tournament. Films and video games Quidditch appears in five of the eight Harry Potter films. Some Quidditch subplots, such as Ron's Keeper storyline in Order of the Phoenix, were cut to save time in the films. Video games that feature Quidditch include: * Harry Potter: Quidditch World Cup * Harry Potter and the Philosopher's Stone * Harry Potter and the Chamber of Secrets * Harry Potter and the Half-Blood Prince * Lego Harry Potter: Years 1–4 * Lego Harry Potter: Years 5–7 In the Harry Potter and the Forbidden Journey attraction in the Wizarding World of Harry Potter at the Islands of Adventure theme park, Quidditch is featured near the end where riders are flown through the Quidditch pitch. A storefront near Ollivanders Wand Shop is themed as a Quidditch supply with a Golden Snitch on the sign and a case containing animated Quaffle and Bludgers surrounded by Beaters' bats. Reception According to David K. Steege, the books "follow very closely the school story tradition of making games and sports central to the boarding school experience; some of the most vivid and popular scenes in the series take place on the playing field." However, some critics have claimed that Rowling's presentation of Quidditch reinforces gender inequality. For example, Heilman and Donaldson argue that the female players ultimately have little impact on the outcome of the game, and it has also been noted that the female players on the Gryffindor Quidditch team have very few lines. This view has been disputed by Mimi R. Gladstein, who points to the presence of female players on the victorious Irish team at the Quidditch World Cup. She argues: "The inclusion of female Quidditch players at the highest level of the sport is done without a trace of self-consciousness and their inclusion isn't an issue within the minds of the characters." On the other hand, D. Bruno Starrs notes Quidditch's rarity as a sport in which males and females compete against each other, and describes it as "levelling" the genders. Quidditch has been criticised for its emphasis on catching the Snitch. Rowling claims that Quidditch is a sport that "infuriates" men in particular, who are bothered by the unrealistic scoring system. Non-fictional Quidditch Quidditch Lane in Lower Cambourne Dedication plaque outside the Bristol Royal Hospital for Children In the real world, the word "Quidditch", long predating Harry Potter, occurs in some English placenames, and seems to come from Anglo-Saxon cwǣð-dīc = "mud-ditch". A street in Lower Cambourne, Cambridgeshire, England is named Quidditch Lane, supposedly after a type of nearby dry ditch called a Quidditch. Fans have been known to visit the area.Village sign attracts Potter fans, BBC News In November 2014, a plaque appeared outside the entrance of Bristol Children's Hospital attesting that the famous hooped sculptures which stand in front of the paediatric institution are, in fact, not a interactive installation inaugurated in 2001, but instead the goalposts used in the 1998 Quidditch World Cup.Sad truth behind Harry Potter fan's adorable prank at Bristol Children's Hospital is revealed, Bristol Post In 2017, "Quidditch" was defined by Oxford Dictionaries, following the inclusion of "Muggle" in the Third (2003) Edition of the Oxford English Dictionary. Oxford Dictionaries associate editor Charlotte Buxton explained that Quidditch had gained recognition beyond the books, pointing to its existence as a real-life sport. As a real-life sport In 2007 the United States Quidditch Association, back then named the Intercollegiate Quidditch Association or (I.Q.A), was founded to regulate quidditch in the United States and abroad, a very popular sport amongst college students. According to the International Quidditch Association, the current international governing body of the sport, the original rules and regulation of the popular collegiate sport known as quidditch were formed ". ... on a sunny Sunday afternoon in 2005 by Xander Manshel and Alex Benepe, students at Middlebury College in Vermont, US". In contrast to the fictional sport, the game is played on foot while using one hand to hold a broom between the legs. Since 2005, many American schools, such as UC Berkeley, have added Quidditch to their list of team sports. In the United States, college teams compete in their respective regions and compete in an annual national tournament, last year held in Texas and won by The University of Texas over runner-ups, The University of California, Berkeley (Cal Quidditch).https://www.usquidditch.org/news/2019/04/winners-of-us-quidditch- cup-12 The sport has since then spread across more than 25 countries and includes multiple international tournaments, including a World Cup. In 2012, the International Quidditch Association held the IQA World Cup, then named the IQA Summer Games, as the torch was passing through Oxford, UK for the Summer Olympics. Gameplay is based on the description in the books, films, and game adaptations, though the sport has been adapted to suit real-world constraints. Quidditch is still evolving to suit safe play for the members of the teams, male and female. Apart from joining teams registered with their national governing body, individuals are also able to become an official certified referee to officiate tournaments and games throughout the year as teams compete to take part in various national and international tournaments. As the oldest national governing body, USQ has hosted a grand total of ten US Quidditch Cups as of 2017. In the United Kingdom, the Quidditch Premier League is played between 10 teams, split between the North and South divisions. In 2017, West Midlands Revolution won the QPL. Real life Quidditch is featured in the movie The Internship. See also * List of fictional sports References Notes Bibliography External links Fictional ball games Harry Potter universe "

❤️ Biproduct 😂

"In category theory and its applications to mathematics, a biproduct of a finite collection of objects, in a category with zero objects, is both a product and a coproduct. In a preadditive category the notions of product and coproduct coincide for finite collections of objects.Borceux, 4-5 The biproduct is a generalization of finite direct sums of modules. Definition Let C be a category with zero morphisms. Given a finite (possibly empty) collection of objects A1, ..., An in C, their biproduct is an object A_1 \oplus \dots \oplus A_n in C together with morphisms *p_k \\!: A_1 \oplus \dots \oplus A_n \to A_k in C (the projection morphisms) *i_k \\!: A_k \to A_1 \oplus \dots \oplus A_n (the embedding morphisms) satisfying *p_k \circ i_k = 1_{A_k}, the identity morphism of A_k, and *p_l \circ i_k = 0, the zero morphism A_k \to A_l, for k eq l, and such that *\left( A_1 \oplus \dots \oplus A_n, p_k \right) is a product for the A_k, and *\left( A_1 \oplus \dots \oplus A_n, i_k \right) is a coproduct for the A_k. In fact, these last two conditions follow from the rest of the definition when n > 0.Saunders Mac Lane - Categories for the Working Mathematician, Second Edition, page 194. An empty, or nullary, product is always a terminal object in the category, and the empty coproduct is always an initial object in the category. Thus an empty, or nullary, biproduct is always a zero object. Examples In the category of abelian groups, biproducts always exist and are given by the direct sum.Borceux, 8 The zero object is the trivial group. Similarly, biproducts exist in the category of vector spaces over a field. The biproduct is again the direct sum, and the zero object is the trivial vector space. More generally, biproducts exist in the category of modules over a ring. On the other hand, biproducts do not exist in the category of groups.Borceux, 7 Here, the product is the direct product, but the coproduct is the free product. Also, biproducts do not exist in the category of sets. For, the product is given by the Cartesian product, whereas the coproduct is given by the disjoint union. This category does not have a zero object. Block matrix algebra relies upon biproducts in categories of matrices.H.D. Macedo, J.N. Oliveira, Typing linear algebra: A biproduct-oriented approach, Science of Computer Programming, Volume 78, Issue 11, 1 November 2013, Pages 2160-2191, , . Properties If the biproduct A \oplus B exists for all pairs of objects A and B in the category C, and C has a zero object, then all finite biproducts exist, making C both a Cartesian monoidal category and a co-Cartesian monoidal category. If the product A_1 \times A_2 and coproduct A_1 \coprod A_2 both exist for some pair of objects A1, A2 then there is a unique morphism f: A_1 \coprod A_2 \to A_1 \times A_2 such that *p_k \circ f \circ i_k = 1_{A_k},\ (k = 1, 2) *p_l \circ f \circ i_k = 0 for k eq l. It follows that the biproduct A_1 \oplus A_2 exists if and only if f is an isomorphism. If C is a preadditive category, then every finite product is a biproduct, and every finite coproduct is a biproduct. For example, if A_1 \times A_2 exists, then there are unique morphisms i_k: A_k \to A_1 \times A_2 such that *p_k \circ i_k = 1_{A_k},\ (k = 1, 2) *p_l \circ i_k = 0 for k eq l. To see that A_1 \times A_2 is now also a coproduct, and hence a biproduct, suppose we have morphisms f_k: A_k \to X,\ k=1,2 for some object X. Define f := f_1 \circ p_1 + f_2 \circ p_2. Then f is a morphism from A_1 \times A_2 to X, and f \circ i_k = f_k for k = 1, 2. In this case we always have *i_1 \circ p_1 + i_2 \circ p_2 = 1_{A_1 \times A_2}. An additive category is a preadditive category in which all finite biproducts exist. In particular, biproducts always exist in abelian categories. References * Additive categories Limits (category theory) "

❤️ Seven Sages of Greece 😂

"Mosaïc of the Seven Sages, Baalbeck, 3rd century A.D., National Museum of Beirut. Calliope at the center, and clockwise from top: Socrates, Chilon, Pittacus, Periander, Cleobulus (damaged section), Bias, Thales, and Solon. The Seven Sages (of Greece) or Seven Wise Men (Greek: hoi hepta sophoi) was the title given by classical Greek tradition to seven philosophers, statesmen, and law-givers of the 6th century BC who were renowned for their wisdom. The Seven Sages The Seven Sages, depicted in the Nuremberg Chronicle Typically the list of the seven sages includes: * Thales of Miletus () is the first well-known Greek philosopher, mathematician, and astronomer. His advice, "Know thyself," was engraved on the front facade of the Temple of Apollo in Delphi. * Pittacus of Mytilene () governed Mytilene (Lesbos). He tried to reduce the power of the nobility and was able to govern with the support of the demos, whom he favoured. * Bias of Priene () was a politician and legislator of the 6th century BC. * Solon of Athens () was a famous legislator and reformer from Athens, framing the laws that shaped the Athenian democracy. * The fifth and sixth sage are variously given as two of: Cleobulus, tyrant of Lindos (), reported as either the grandfather or father-in-law of Thales; Periander of Corinth (b. before 634 BC, d. ); Myson of Chenae (6th century BC); Anacharsis the Scythian (6th century BC). * Chilon of Sparta () was a Spartan politician to whom the militarization of Spartan society was attributed. Diogenes Laërtius points out, however, that there was among his sources great disagreement over which figures should be counted among the seven.Diogenes Laërtius, i. 41 Perhaps the two most common substitutions were to exchange Periander or Anacharsis for Myson. On Diogenes' first list of seven, which he introduces with the words "These men are acknowledged wise," Periander appears instead of Myson;Diogenes Laërtius, i. 13 the same substitution appears in The Masque of the Seven Sages by Ausonius.Ausonius, The Masque of the Seven Sages Both Ephorus and Plutarch (in his Banquet of the Seven Sages) substituted Anacharsis for Myson. Diogenes Laërtius further states that Dicaearchus gave ten possible names, Hippobotus suggested twelve names,Diogenes Laërtius, i. 42 and Hermippus enumerated seventeen possible sages from which different people made different selections of seven. Leslie Kurke contends that "Aesop was a popular contender for inclusion in the group"; an epigram of the 6th century AD poet Agathias (Palatine Anthology 16.332) refers to a statue of the Seven Sages, with Aesop standing before them.Leslie Kurke, Aesopic Conversations: Popular Tradition, Cultural Dialogue, and the Invention of Greek Prose, Princeton University Press, 2010, pp. 131–2, 135. Interpretations Earliest passage in which the Seven Wise Men are mentioned together, from Oxyrhynchus Papyri. In Plato's Protagoras, Socrates says: The section of the Protagoras in which appears this passage is "elaborately ironical", making it unclear which of its parts may be taken seriously,p. 156, James Adam, Platonis Protagoras, Cambridge University Press, 1893; p. 83, C.C.W. Taylor, Plato: Protagoras, Oxford University Press, 2002. The words "elaborately ironical" are Adam's. Diogenes Laërtius in his account of the life of Pyrrho, the founder of Pyrrhonism that the Seven Sages of Greece were considered to be precursors of Pyrrho's philosophical skepticism because the Delphic Maxims were skeptical. "The maxims of the Seven Wise Men, too, they call skeptical; for instance, "Observe the Golden Mean," and "A pledge is a curse at one's elbow," meaning that whoever plights his troth steadfastly and trustfully brings a curse on his own head."Diogenes Laërtius Lives of the Eminent Philosophers Book IX, Chapter 11, Section 71 https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_IX#Pyrrho Sources and legends The oldestA. Griffiths, "Seven Sages", in Oxford Classical Dictionary (3rd ed.). All the sources are collected in Bruno Snell, Leben und Meinungen der Sieben Weisen. Griechische und lateinische Quellen erläutert und übertragen. Munich, 1971. explicit mention on record of a standard list of seven sages is in Plato's Protagoras, quoted above. Diogenes Laërtius reported that there were seven individuals who were held in high esteem for their wisdom well before Plato's time. According to Demetrius Phalereus, it was during the archonship of Damasias (582/1 BC) that the seven first become known as "the wise men", Thales being the first so acknowledged.Kirk, Raven, & Schofield, The Presocratic Philosophers (Cambridge, 1983, 2nd edition), p. 76, citing Diogenes Laërtius, i. 22. Later tradition ascribed to each sage a pithy saying of his own, but ancient as well as modern scholars have doubted the legitimacy of such ascriptions.H. Parke and D. Wormell, The Delphic Oracle, (Basil Blackwell, 1956), vol. 1, pp. 387–389. A compilation of 147 maxims, inscribed at Delphi, was preserved by the fifth century AD scholar Stobaeus as "Sayings of the Seven Sages,"Kurke, p. 109. but "the actual authorship of the...maxims set up on the Delphian temple may be left uncertain. Most likely they were popular proverbs, which tended later to be attributed to particular sages."Parke & Wormell, p. 389. In addition to being credited for pithy sayings, the wise men were also apparently famed for practical inventions; in Plato's Republic (600a), it is said that it "befits a wise man" to have "many inventions and useful devices in the crafts or sciences" attributed to him, citing Thales and Anacharsis the Scythian as examples. According to a number of moralistic stories, there was a golden tripod (or, in some versions of the story, a bowl or cup) which was to be given to the wisest. Allegedly, it passed in turn from one of the seven sages to another, beginning with Thales, until one of them (either Thales or Solon, depending on the story) finally dedicated it to Apollo who was held to be wisest of all.Diogenes Laërtius i. 27ff.; R. Martin, "Seven Sages", Encyclopedia of Classical Philosophy (ed. D. Zeyl, 1997), p. 487; Parke & Wormell, pp. 387–388 According to Diogenes, Dicaearchus claimed that the seven "were neither wise men nor philosophers, but merely shrewd men, who had studied legislation."Diogenes Laërtius, i. 40. And according to at least one modern scholar, the claim is correct: "With the exception of Thales, no one whose life is contained in [Diogenes'] Book I [i.e. none of the above] has any claim to be styled a philosopher."p. 42 note a, R. Hicks, Diogenes Laërtius: Lives of Eminent Philosophers, vol. 1, Harvard University Press, 1925. See also *Sage (sophos) *Saptarishi References External links Plutarch's The Dinner of the Seven Wise Men, in the Loeb Classical Library. * Seven Sages of Greece with illustrations and further links. * Jona Lendering's article Seven Sages includes a chart of various canonical lists. * Sentences of the Seven Sages Ancient Greek philosophers Ancient Greek titles Ancient Greeks Articles about multiple people in ancient Greece Classical studies History of education History of ideas History of philosophy History of science Septets "