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 …

Nov 22, 2012 · However, a Homomorphism need not be bijective like an isomorphism. For example the exponential map from the set of real numbers with the $+$ operation to the set of non -zero real …

Mar 30, 2011 · My question is: what exactly is the difference between homomorphism and a linear map? I can see that linearity is defined in terms of a vector space or module and homomorphism in terms …

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 …

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 …

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 …

23 Clearly the kernel of a group homomorphism is normal (proof), but I often hear my professor mention that any normal subgroup is the kernel of some homomorphism. This feels correct but isn't entirely …