Dec 31, 2015 · Then each morphism is like the reverse of a function. In particular, there are 2 distinct morphisms from {x,y} to {x} even though there is only one such function.

To answer your main question pedantically: broadly speaking, a morphism is an arrow between two objects. One will usually require morphisms to preserve some structure present in the objects of the …

Nov 5, 2016 · 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 …

May 22, 2016 · 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 …

A morphism is an arrow from some specific object to some specific other object. An endofunctor contains the data of a function from the collection of objects in some category to itself. I think you …

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 …

But the equivalent condition to surjectivity in the statement of the lemma still makes perfect sense in an arbitrary category, so that statement is a natural generalization to take as the definition of a …

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 …

Sep 4, 2020 · 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 …

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...