Adjunction

Functors: $F:\mathcal{C}\leftrightarrows \mathcal{D}:G$

An adjunction: $F⊣G$ if:

$${\text{Hom}}_{\mathcal{D}}(F(A),B)\cong {\text{Hom}}_{\mathcal{C}}(A,G(B))$$

Naturally in both $A$ and $B$.

• $F$ is left adjoint, $G$ right adjoint.
• Unit: $\eta :\text{Id}\Rightarrow G\circ F$
• Counit: $\epsilon :F\circ G\Rightarrow \text{Id}$

See also

• Functor
• Category
• Natural Transformation
• Monad