Left (resp. right) adjoint functor fully faithful iff unit (resp. counit) isomorphism
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?
97608
Showing a Ring of endomorphisms is isomorphic to a Ring
87412
when does a functor map products into products?
6385
Minimal counterexamples of the isomorphism problem for integral group rings
39763
Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure
61593
Adjoint map is Lie homomorphism
153508
Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.
146690
Basis for adjoint representation of $sl(2,F)$
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
33063
Are all simple left modules over a simple left artinian ring isomorphic?
44396
Noetherian Ring under a Homomorphism / homomorphic function / map
60514
Isometric  Left Inverse Adjoint
86748
Isomorphism of hom sets implies objects are isomorphic
7441
Hom is a left-exact functor
143517
Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
52554
Showing that localization is an exact functor
25383
Morphism between quotient sheaf ($K_{X}/\mathcal{O}_{X}$) and $\bigoplus_{x\in\mathcal{X}}i_{x,*}(K(X)/\mathcal{O}_{X,x})$