Semidirect Products of Monoidal Categories
Ben Fuller
TL;DR
This paper introduces semidirect products of skew monoidal categories, extending the concept of semidirect products from groups to categories, and explores their structural properties and examples.
Contribution
It defines semidirect products for skew monoidal categories and analyzes their interaction with various monoidal structures, providing new categorical constructions.
Findings
Semidirect products of skew monoidal categories are introduced.
Examples of monoidal categories that are left closed but not right closed are provided.
The interaction with monoidal, autonomous, and closed structures is characterized.
Abstract
We introduce semidirect products of skew monoidal categories as a categorification of semidirect products of monoids (or, perhaps more familiarly, of groups). We also discuss how this construction interacts with monoidal, autonomous and closed monoidal structures. We end by producing some examples of monoidal categories which are left closed but not right closed.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Operator Algebra Research