An Introduction to Adjunction

Kosta Došen

This is an introduction to the notion of adjunction from . an abstract point of view. A systematic survey is made of various definitions of this notion, including two definitions not recorded in the literature. A similar survey is also made of the definitions of comonad, which also includes new material. Finally, the relationship between the notion of adjunction and the notion of comonad is explained through two adjunctions involving the category of adjunctions and the category of comonads, where the latter category is isomorphic to a full subcategory of the former. The+ standard presentation of this relationship, through the category of resolutions of a comonad, is a corollary of this new presentation of the matter.