Right adjoint is fully faithful iff the counit is an isomorphism (without Yoneda)
49789
Let $C,D$ be categories and $F:C\to D$ and $G:D\to C$ be adjoint functors. Then $F$ is fully faithful iff the unit is an isomorphism?
123419
Abstract algebra: homomorphism and an element of a prime order
135422
$\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
25260
Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
152887
Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
2439
If a linear operator has an adjoint operator, it is bounded
81423
Completeness and Topological Equivalence
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
25728
A second isomorphism theorem for action on cosets
42941
Pair of adjoint functors and showing that two certain maps are inverses
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
151993
Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
151047
a non trivial example: $G/H$ is isomorphic to $G$
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
134458
Isomorphisms preserving integral domains and fields
124003
Composition of adjoint functors
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity