How to prove an equivalent definition of injective?
121993
Prove that $f$ is one-to-one iff $f \circ h = f \circ k$ implies $h = k$.
113065
Proving equivalences of statements equivalent to AC
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
82689
Monos in $\mathsf{Mon}$ are injective homomorphisms.
96202
Prove composition of bijections is bijection
93040
$f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
122814
Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
49882
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
82655
Number of Injective Maps
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
20030
Is an equivalence an adjunction?
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
157268
Proving a bijection with absolute value
66548
proving topological equivalence
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse