What is the meaning of Adjunction?

The act of joining; the thing joined or added.

The joining of personal property owned by one to that owned by another.

The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.

A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.

A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.

1. (formally, given two categories ${\displaystyle {\mathcal {C}}}$ and ${\displaystyle {\mathcal {D}}}$ and (covariant) functors ${\displaystyle F:{\mathcal {C}}\rightarrow {\mathcal {D}}}$ and ${\displaystyle G:{\mathcal {D}}\rightarrow {\mathcal {C}}}$) A natural isomorphism ${\displaystyle \Phi$ :\operatorname {Hom} _{\mathcal {C}}(G\cdot ,\cdot )\to \operatorname {Hom} _{\mathcal {D}}(\cdot ,F\cdot )} (where the hom-functors are understood as bifunctors from ${\displaystyle {\mathcal {D}}^{\operatorname {op} }\times {\mathcal {C}}}$ to ${\displaystyle \mathbf {Set} }$). See Adjoint functors on Wikipedia.Wikipedia .

   (formally, given two categories ${\displaystyle {\mathcal {C}}}$ and ${\displaystyle {\mathcal {D}}}$ and (covariant) functors ${\displaystyle F:{\mathcal {C}}\rightarrow {\mathcal {D}}}$ and ${\displaystyle G:{\mathcal {D}}\rightarrow {\mathcal {C}}}$) A natural isomorphism ${\displaystyle \Phi$ :\operatorname {Hom} _{\mathcal {C}}(G\cdot ,\cdot )\to \operatorname {Hom} _{\mathcal {D}}(\cdot ,F\cdot )} (where the hom-functors are understood as bifunctors from ${\displaystyle {\mathcal {D}}^{\operatorname {op} }\times {\mathcal {C}}}$ to ${\displaystyle \mathbf {Set} }$). See Adjoint functors on Wikipedia.Wikipedia .

   Source: wiktionary.org