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  • category theory - How is a morphism different from a function . . .
    A morphism in the categorical sense does pretty much the same (and indeed is also called an arrow), except for the fact that relations are defined on sets whereas in categories you work with classes and for the fact that a relation establishes a specific "set of arrows" whereas a morphism refers to all possibile arrows between two distinct objects
  • What is the difference between Mapping and Morphism
    A morphism is a concept introduced in the language of categories to designate one element of the set Hom (X, Y) where X and Y are two objects of said category So if we talk about the category of sets, a morphism is just a mapping if we talk about category of groups, a morphism is a group homomorphism ie mapping that complies with the laws of the groups in question Morphism of ring is ring
  • What is the distinction between morphism and functor really?
    So, morphism: an arrow between two categories functor: what goes between categories and here, "what" means morphism because defining a category which uses only one collection (representing the collection of morphisms) Accordingly, morphism == functor, and usually we use the identical concept in different words everywhere (mostly with many
  • Examples of morphisms of schemes to keep in mind?
    What are interesting and important examples of morphisms of schemes (especially varieties) to keep in mind when trying to understand a new concept or looking for a counterexamples? Examples of wha
  • algebraic geometry - What does this notion of scheme morphism mean . . .
    As you know, a scheme consists of two pieces of data: a topological space and a sheaf of local rings (locally isomorphic to spectra of commutative rings, of course) A morphism of schemes is just a morphism of locally ringed spaces, which again consists of two parts: a continuous map of topological spaces and a map of the structure sheaves For the case of affine and projective varieties we
  • Inverses of Morphisms Necessarily Being Morphisms
    Inverses of morphisms are morphisms by definition What you're asking is a little different, though: you're asking when, in a category whose objects are sets with additional structure, the set-theoretic inverse of a morphism is necessarily also a morphism (in the sense of preserving the additional structure) The right way to set up this question is to make explicit the use of the forgetful
  • What does homomorphism require that morphism doesnt?
    Hence, they chose morphism as being close enough to homomorphism to be suggestive, but not identical, so that it didn't give the psychological impression of ruling out contexts like topological spaces and continuous maps





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