nLab
symmetric endofunctor

Idea

A symmetric endofunctor is an endofunctor together with actions of the symmetric groups on its automorphism groups.

Definition

Let Φ\Phi be a graded monoid in the category of groups, e.g. the graded monoid Σ=(Σ n) n0\Sigma = (\Sigma_n)_{n \ge 0} of symmetric groups.

A symmetric endofunctor F:CCF : C \to C is an endofunctor together with the data of, for each nNn \in \mathbf{N}, a group homomorphism

Φ nAut(F n) \Phi_n \to \Aut(F^{\circ n})

where F nF^{\circ n} is the nn-fold composite of FF.

Created on February 7, 2014 at 00:55:15. See the history of this page for a list of all contributions to it.