Are two objects equivalent in a category when their hom sets are isomorphic?
86748
Isomorphism of hom sets implies objects are isomorphic
115649
Proving two sets $A, B$ are order isomorphic
47617
Are groups with all the same Hom sets already isomorphic?
70658
Isomorphism between quotient modules
28154
Riehl's Category Theory in Context - Exercise 2.1.iv.
34300
"Natural" categories where monomorphisms differ from injective morphisms
148881
Aut(GxH) isomorphic to Aut(G)xAut(H)
126790
Basic Isomorphism Question
127826
Is the geometric realization of a pointed category contractible?
74455
Can a single sentence be used to distinguish between isomorphic classes of finite structures?
53687
Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?
70797
Why doesn't the definition of a category require an explicit notion of morphisms equality?
39576
Quotient ring being isomorphic to the initial ring
20556
Isomorphism between two models of Hilbert's Axioms with different notions of congruence
93017
Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
69384
Are the following modules free and/or isomorphic?
136210
There is more than one functor that fix objects in category of groups?