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Adjunction

Adjunction

Aug 11, 20231 min read

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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.


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