nLab dynamical extension of a monoidal category

Idea

Given a monoid LL in a monoidal category, there is an induced monad T LT^L obtained by tensoring with LL from the right. Consider the Kleisli category of the monad T LT^L. It is not necessarily a monoidal category; there is a need for an additional structure (distributive law of a sort) in order to make such a lift. If the monoidal category CC in question is the monoidal category of left modules over a Hopf algebra HH, then any commutative algebra LL in the center Z(C)Z(C) provides a canonical lift to the Kleisli category

Physical motivation

Dynamical extension or a dynamization of a monoidal category is an abstract framework to aid the construction of so called dynamical quantum groups which are in turn related to dynamical quantum Yang-Baxter equation.

Definition

Properties and remarks

In Donin-Mudrov (2006) a relation to bialgebroids has been exhibited.

Literature

Last revised on September 28, 2024 at 13:59:29. See the history of this page for a list of all contributions to it.