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.

Given a pair of categories ${\mathcal {C}}$ and ${\mathcal {D}}$ : an anti-parallel pair of functors $F:{\mathcal {C}}\rightarrow {\mathcal {D}}$ and $G:{\mathcal {D}}\rightarrow {\mathcal {C}}$ and a natural transformation ${\displaystyle \eta$ called “unit” such that for any object $A\in {\mathcal {C}}$ , for any object $B\in {\mathcal {D}}$ , and for any morphism $f:A\rightarrow GB$ , there is a unique morphism $g:FA\rightarrow B$ such that $Gg\circ \eta _{A}=f$ . (Note: there is another natural transformation called “counit” as well but its existence may be derived by theorem.) The pair of functors express a similarity between the pair of categories which is weaker than that of an equivalence of categories.

↑ Michael Barr with Charles Wells (1995) Category Theory for Computing Science, second edition, University Press, Cambridge, Great Britain: Prentice Hall, →ISBN, §9.2, page 258

Source: wiktionary.org

What is the meaning of Adjunction?

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