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Ends Him Back
End, END, Ending, or ENDS may refer to: End Mathematics *End (category theory) *End (topology) *End (graph theory) *End (graph_theory)#Cayley_graphs, End (group theory) (a subcase of the previous) *End (endomorphism) 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 Entertainment *End (band) an American hardcore punk supergroup *End key on a modern computer keyboard *End Poem, a narrative written by Julian Gough for ''Minecraft'' *End Records, a record label *"End", a song by The Cure from ''Wish (The Cure album), Wish'' * Ends (song), "Ends" (song) a 1998 song by Everlast, off the album ''Whitey Ford Sings the Blues'' * End (album), ''End'' (album), by Explosions in the Sky * Ends (Spaced), "Ends" (''Spaced''), a television episode Other uses *End, in weaving, a single thread of the Warp (weaving), warp *''Ends (short story collection)'' (1988 book) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
End (category Theory)
In category theory, an end of a functor S:\mathbf^\times\mathbf\to \mathbf is a universal dinatural 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 category, complete and C is small, the end can be described as the Equalizer (mathematics)#In category theory, 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |