The injectivity of $f\mapsto f\circ v$ on $\hom(M'',N)$ implies that $v$ is surjective
16656
Atiyah and Macdonald, Proposition 2.9
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
20199
Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
115999
Is there always an injective map from a space in its dual space?
5802
Proving the universal mapping property for polynomial rings
111689
Surjective, but not injective endomorphism
5635
How to prove that the Frobenius endomorphism is surjective?
16610
Surjectivity of a map from a space to itself
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
152212
Prove that the natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$ is an isomorphism
157378
On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
126472
Surjective endomorphisms of uniserial modules
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
53971
If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.