Mario Román

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Adjunction

Adjunction

Apr 29, 20251 min read

  • adjunction - reducing an adjunction
  • adjunction - sliced left adjoint
  • adjunction - name the adjunction, not its components
  • adjunction - multivariable adjunction
  • 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.

Tags: category theory.


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  • 2-Duality, lax and strong
  • Polarization of a monoidal category
  • quasi 2-adjunction
  • Multivariable adjunction
  • name the adjunction, not its components
  • reducing an adjunction
  • Sliced left adjoint
  • Adjunction
  • arrow notation
  • collage of an adjunction
  • Duality
  • failure of associativity on an adjunction collage
  • formal 2-adjunction
  • monadicity theorem

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