what exactly is an isomorphism? - Mathematics Stack Exchange
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 …
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 …
linear algebra - Difference between epimorphism, isomorphism ...
Can somebody please explain me the difference between linear transformations such as epimorphism, isomorphism, endomorphism or automorphism? I would appreciate if somebody …
What's an Isomorphism? - Mathematics Stack Exchange
Feb 11, 2016 · To expand a bit on what @BrianO said, isomorphisms differ between different kinds of objects. Broadly speaking, isomorphisms preserve "structure" between objects, but …
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.
Questions on isomorphism of graphs - Mathematics Stack Exchange
Dec 9, 2024 · I think testing isomorphism between two graphs can be done by just checking their connectivity without the use of labels. However, the definition of isomorphism as a map …
basic difference between canonical isomorphism and isomorphims
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 …
soft question - What is an Isomorphism: Linear algebra
Mar 23, 2015 · An isomorphism is a bijective homomorphism. "Structure" can mean many different things, but in the context of linear algebra, almost exclusively means the vectorial …
Why are two isomorphic objects "categorically the same"?
Jan 29, 2019 · So isomorphic structures can and should be considered the same. Also, when we fix the isomorphism we can identify elements of the two structures that are related by the …
Difference between "≈", "≃", and "≅" - Mathematics Stack Exchange
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. …