Is a homomorphism a general term that could mean different things, or does it have a specific definition? Also, could someone give me an example in which homomorphisms are useful, and what is an …

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 …

The word isomorphism is related to category, in which you work. For example, if you work in the category $\mathbf {Top}$ of topological spaces, the words isomorphism and homeomorphism are …

13 "Homomorphism" means different things depending on what objects you're thinking about, and one of those things is the same as "linear map." Namely, for a field k k, a k k -linear map between two k k …

Nov 11, 2022 · Homomorphism: A homomorphism is a structure preserving map, which in a vector space, is equivalent to being a linear map. Isomorphism: (same as homeomorphism) A bijective map …

A homomorphism is a special kind of map between two groups because homomorphism respect the group operation. An isomorphism is a bijective map which maintain the equivalence of the underlying …

Sep 23, 2019 · Here, seeing precisely three elements of the same cycle-type, we know there is a homomorphism from S4 S 4 to a subgroup of S3 S 3 induced by this action - the action of …

Nov 15, 2015 · Roughly speaking, a homomorphism is a map which respects the underlying structure of the set. In the case of a group it means the map changes a product into a product. If the notation is …

I'm not interested in the answer in particular, mostly I'm concerned about understanding the properties of homomorphism, so I can answer these kind of questions myself. So, first of all, I know that …