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 theory.

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 to mind is …

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

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. At least, …

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 "bijection v …

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 between two …

An example of a "natural" isomorphism is the canonical isomorphism between a finite-dimensional vector space V V and its double-dual V∗∗ V ∗ ∗. Again, this is natural because the double-dual (−)∗∗ …

Jun 20, 2019 · In categories of algebras yes, a morphism that is bijective on underlying sets is always an isomorphism (invertible morphism). You want to restrict to algebras-and-operations, as relational …

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 that two …