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End Sign Eupalinian Aqueduct
End, END, Ending, or variation, may refer to: End *In mathematics: **End (category theory) **End (topology) **End (graph theory) ** End (group theory) (a subcase of the previous) **End (endomorphism) *In sports and games **End (gridiron football) **End, a division of play in the sports of curling, target archery and pétanque **End (dominoes), one of the halves of the face of a domino tile *In entertainment: **End (band) an American hardcore punk supergroup formed in 2017. **End key on a modern computer keyboard **End Records, a record label **"End", a song by The Cure from ''Wish'' ** Ends (song) (1998 song) song by Everlast, off the album ''Whitey Ford Sings the Blues'' *In other areas: **End, in weaving, a single thread of the warp **''Ends (short story collection)'' (1988 book) anthology of Gordon R. Dickson stories END * European Nuclear Disarmament * Endoglin, a glycoprotein * Equivalent narcotic depth, a concept used in underwater diving * Environmental noise directive * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
End (category Theory)
In category theory, an end of a functor S:\mathbf^\times\mathbf\to \mathbf is a universal extranatural transformation from an object ''e'' of X to ''S''. More explicitly, this is a pair (e,\omega), where ''e'' is an object of X and \omega:e\ddot\to S is an extranatural transformation such that for every extranatural transformation \beta : x\ddot\to S there exists a unique morphism h:x\to e of X with \beta_a=\omega_a\circ h for every object ''a'' of C. By abuse of language the object ''e'' is often called the ''end'' of the functor ''S'' (forgetting \omega) and is written :e=\int_c^ S(c,c)\text\int_\mathbf^ S. Characterization as limit: If X is complete and C is small, the end can be described as the equalizer in the diagram :\int_c S(c, c) \to \prod_ S(c, c) \rightrightarrows \prod_ S(c, c'), where the first morphism being equalized is induced by S(c, c) \to S(c, c') and the second is induced by S(c', c') \to S(c, c'). Coend The definition of the coend of a functor S:\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |