Example of a monomorphism and epimorphism that is not isomorphism.
118354
Epimorphism and Monomorphism = Isomorphism?
132571
Local homeomorphisms which are not covering map?
151287
Isomorphic abelian groups which are not isomorphic R-modules
108408
Example of quotient mapping that is not open
153852
Example of modules that are projective but not free; torsion-free but not free
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
133664
When the automorphism group is trivial......
24828
surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
82689
Monos in $\mathsf{Mon}$ are injective homomorphisms.
121945
Monomorphisms and Epimorphisms in the category of small categories
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
87983
Examples of Separable Spaces that are not Second-Countable
83744
is there a property of a category that is preserved by category isomorphism, but not equivalence?
101064
Showing the triviality of homomorphisms
25874
Showing that a certain map is not flat by explicit counterexample