Why is $A\rightarrow \operatorname{im}(f)$ an epimorphism in an abelian category
51245
$A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category
13764
Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
128673
Given $A : \mathcal{C} \rightarrow \mathcal{E}$, when does $\operatorname{colim} A = A(1)$?
6904
questions about extremal epimorphisms in category theory
152678
I've read that abelian categories can naturally be enriched in $\mathbf{Ab}.$ How does this actually work?
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
145462
On the canonical isomorphism between $V$ and $V^{**}$
97608
Showing a Ring of endomorphisms is isomorphic to a Ring
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
98436
Finite order endomorphisms
145339
Index of the subgroup $\operatorname{Im}(f)$
149849
Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
106347
Why is the image of a homomorphism a subgroup of the codomain?
135422
$\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
148616
When is a ring homomorphism $A \to A$ surjective but not injective.