Adjunctions are dualities in the bicategory of categories.
See also.
- Adj, the category of adjunctions
- adjunctions compose
- duality
- monadic adjunction
- reducing an adjunction
- sliced left adjoint
- name the adjunction, not its components
- multivariable adjunction
- decategorifying multivariable adjunctions
- adjunction - graphical calculus for multivariable adjunctions
- collage of an adjunction
- adjunction - polycategory of multivariable adjunctions
- adjunction - the 2-polycategorical structure of multivariable adjoints
- adjunction - pseudomonoids of multivariable adjunctions are closed categories
- For any adjunction, the right adjoint is full and faithful if and only if the counit is an isomorphism.
- The components of the unit are monomorphisms if and only if the left adjoint functor is faithful.
References.
- Categories for the Working Mathematician (MacLane, 1971)
- Category Theory Using String Diagrams (Marsden, 2014), for a practical presentation of string diagrams.
Tags: category theory.