nLab pseudoaction



Categorical algebra

Representation theory



Pseudoactions are categorified actions. In other words, they are coherent actions of pseudomonoids.


  1. A pseudomonoid in (Cat,1,×)(\mathbf{Cat}, 1, \times) is exactly a monoidal category. The pseudoaction of a monoidal category on a category is an actegory.
  2. A pseudomonoid in (Fib,1,×)(\mathbf{Fib}, 1, \times) is a monoidal fibration. Pseudoactions of a monoidal fibration on a fibration are considered in (Vasilakopoulou ‘18).
  3. A pseudomonad is a pseudomonoid in the Gray monoid of endomorphisms of an object in a Gray-category (see (Marmolejo ‘99, Definition 3.1)). A pseudoalgebra of a pseudomonad is a pseudoaction of the pseudomonad on the functor picking out the carrier of the pseudoalgebra.

See also


Last revised on October 7, 2023 at 09:11:45. See the history of this page for a list of all contributions to it.