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 …

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

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

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. …

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 …

15 Proving that two groups are isomorphic is a provably hard problem, in the sense that the group isomorphism problem is undecidable. Thus there is literally no general algorithm for proving …

It's also natural in the technical sense: there is a natural transformation $\eta$ from the identity functor to the double-dual functor $ (-)^ {**}$, and the component $\eta_V : V \to V^ {**}$ of …

Dec 12, 2014 · As Cameron says, an isomorphism is a structure-preserving bijection, like a group isomorphism, which is a bijection that preserves the group structure. Or ring isomorphisms.