what exactly is an isomorphism? - Mathematics Stack Exchange 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
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 to mind is topological homeomorphism, but here we are talking about algebraic structures, and topological spaces are not algebraic structures
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 can explain the idea with examples or guide to some good source to clear the concept
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 At least, this is the convention used in this book and by most category theorists, although it is far from universal in mathematics at large
Questions on isomorphism of graphs - Mathematics Stack Exchange 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 between two sets forces me to think that elements in each set need to be distinguishable by some use of label Otherwise, how do we express which one is being mapped to which?
Whats an Isomorphism? - Mathematics Stack Exchange To expand a bit on what @BrianO said, isomorphisms differ between different kinds of objects Broadly speaking, isomorphisms preserve "structure" between objects, but what this "structure" is depends very much on whether you are talking about groups, vector spaces, algebras, etc Hence it's difficult to say what properties are preserved in general by isomorphisms
basic difference between canonical isomorphism and isomorphims 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 geometric object
Bijective vs Isomorphism - Mathematics Stack Exchange 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 isomorphism"