例句與造句

1. From these axioms, one can prove that there is exactly one identity morphism for every object.
2. There is no longer any notion of an identity morphism, nor of a particular composition of two morphisms.
3. Some authors use a slight variation of the definition in which each object is identified with the corresponding identity morphism.
4. The identity morphism ( identity mapping ) is called the "'trivial automorphism "'in some contexts.
5. Such a definition generalizes to the concept of an identity morphism in category theory, where the endomorphisms of need not be functions.
6. It's difficult to find identity morphism in a sentence. 用identity morphism造句挺難的
7. An idempotent is said to'split'if it can be factored as fg, where gf is an identity morphism in a category.
8. For a concrete category ( that is the objects are sets with additional structure, and of the morphisms as structure-preserving functions ), the identity morphism is just the identity function, and composition is just the ordinary composition of functions . " Associativity " then follows, because the composition of functions is associative.
9. By considering the pullback square of f and T, which pulls back to an object U and morphism u : U \ to \ Omega and the unique morphism U \ to 1 say, and the pullback square of morphisms T and u to some object V ( and the composite of these 2 pullback squares,'joined'by u ), show that f \ circ f is the identity morphism : 1 _ { \ Omega }.
10. Any monoid ( any algebraic structure with a single associative binary operation and an identity element ) forms a small category with a single object " x " . ( Here, " x " is any fixed set . ) The morphisms from " x " to " x " are precisely the elements of the monoid, the identity morphism of " x " is the identity of the monoid, and the categorical composition of morphisms is given by the monoid operation.