Aug 4, 2021 · An isomorphism within a partial order is an equality. If there is an isomorphism between two objects, then they are totally indistinguishable from the perspective of category …

Isomorphism is a bijective homomorphism. I see that isomorphism is more than homomorphism, but I don't really understand its power. When we hear about bijection, the first thing that comes …

An isomorphism is a homomorphism that can be reversed; that is, an invertible homomorphism. So a vector space isomorphism is an invertible linear transformation.

Dec 9, 2024 · I think testing isomorphism between two graphs can be done by just checking their connectivity without the use of labels. However, the definition of isomorphism as a map …

Can somebody please explain me the difference between linear transformations such as epimorphism, isomorphism, endomorphism or automorphism? I would appreciate if somebody …

Apr 26, 2019 · What is the basic difference between canonical isomorphism and isomorphims? I need some basic analysis. As far as I consider on canonical isomorphism means a similarity …

Apr 15, 2020 · Another difference between "bijective" and "isomorphism" is that bijective is an adjective but isomorphism is a noun. It would be better to ask "bijective v isomorphic" or …

Isomorphism is an algebraic notion, and homeomorphism is a topological notion, so they should not be confused. The notion of homeomorphism is in connection with the notion of a …

The symbol ≅ is used for isomorphism of objects of a category, and in particular for isomorphism of categories (which are objects of CAT). The symbol ≃ is used for equivalence of categories. …

Jan 21, 2025 · An isomorphism in the category of $\mathbf {Sets}$ is just a bijection (there being no additional structure to preserve). I agree that it's a bit unusual to use the term in that way, …