Partial actions of groups on monoidal categories

TL;DR

This paper introduces the concept of partial group actions on monoidal categories, extending existing algebraic notions to a categorical setting with new constructions like globalization and partial invariants.

Contribution

It defines partial group actions on monoidal categories and develops analogous constructions to those in algebra, broadening the scope of partial action theory.

Findings

Defined partial actions of groups on monoidal categories.

Constructed globalization and partial invariants in this context.

Extended algebraic partial action concepts to categorical frameworks.

Abstract

In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra such as the globalization, the subalgebra of partial invariants, and the partial smash product.