Proving for two naturally isomorphic functors, if one is full, then so is the other.
140503
What properties do natural isomorphisms between functors preserve?
72103
Failure of isomorphisms on stalks to arise from an isomorphism of sheaves
98992
A morphism of sheaves of sets is an isomorphism if it induces an isomorphism of all stalks.
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
52556
Isomorphism of $S^1$.
125982
If the dual spaces are isometrically isomorphic are the spaces isomorphic?
45270
Surjective endomorphisms of finitely generated modules are isomorphisms
59995
Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.
142698
Proving that the fundamental groups of two spaces with same homotopy type are isomorphic
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
115663
Proving an isomorphism using the isomorphism theorems
145462
On the canonical isomorphism between $V$ and $V^{**}$
83109
Formation of the free group on $S$ is a functor
102371
Proving that two vector spaces of equal dimension are isomorphic
40793
What is the difference betwen equivalence and isomorphism of functors in categories.