Hopf categories associated to comonoidal functors

TL;DR

This paper constructs Hopf categories linked to comonoidal functors, extending previous work on Hopf monoids, with applications to Lie bialgebras and deformed categories.

Contribution

It introduces an explicit construction of Hopf categories associated to comonoidal functors, generalizing era's Hopf monoid construction.

Findings

Hopf categories can be explicitly constructed from comonoidal functors

The construction applies to Lie bialgebra twists

Results extend to deformed categorical settings

Abstract

We provide an explicit construction of Hopf categories associated to comonoidal functors, generalizing \v{S}evera's construction of Hopf monoids through M-adapted functors. We discuss the example of the Hopf category whose underlying class is the set of twists of a Lie bialgebra. Finally, we apply the result to the setting of deformed categories.