what exactly is an isomorphism? - Mathematics Stack Exchange
2021年8月4日 · An isomorphism picks out certain traits of one object, certain traits of the other, and shows that the two objects are the same in that specific way. Two sets are "isomorphic" …
linear algebra - Difference between epimorphism, isomorphism ...
Isomorphism: a homomorphism that is bijective (AKA 1-1 and onto); isomorphic objects are equivalent, but perhaps defined in different ways Endomorphism : a homomorphism from an …
What is the difference between homomorphism and isomorphism?
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 …
basic difference between canonical isomorphism and isomorphims
2019年4月26日 · The isomorphism requires something specific to this vector space in order to define it. But we don't require that to define this isomorphism $\phi$ of a vector space with its …
terminology - What does "isomorphic" mean in linear algebra ...
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 idea of an invertible …
What's the difference between isomorphism and homeomorphism?
Isomorphism (in a narrow/algebraic sense) - a homomorphism which is 1-1 and onto. In other words: a homomorphism which has an inverse. In other words: a homomorphism which has an …
What's the difference between a bijection and an isomorphism?
2014年12月12日 · If you are talking just about sets, with no structure, the two concepts are identical. Usually the term "isomorphism" is used when there is some additional structure on …
soft question - What is an Isomorphism: Linear algebra
2015年3月23日 · A homomorphism is a structure-preserving mapping. An isomorphism is a bijective homomorphism. "Structure" can mean many different things, but in the context of …
Why is the kernel of an isomorphism always equal to the identity?
According to my source, we have $$\text{Ker}(f)=\{g\in G:f(g)=e_{G'}\},$$ and for an isomorphism we always have $$\text{Ker}(f)=\{e_G\}.$$ I know that an isomorphism is a bijection and get …
Why are two isomorphic objects "categorically the same"?
2019年1月29日 · The point is that you need the notion of natural isomorphism for defining equivalences but you do not need to believe that isomorphic objects are the same. The small …