Enrichments over symmetric Picard categories
V. Schmitt
TL;DR
This paper introduces the concept of 2-modules over symmetric Picard categories, extending the theory of categorical rings (2-rings) and providing foundational results in this emerging area.
Contribution
It presents the basic definitions and initial results on 2-modules over symmetric Picard categories, advancing the understanding of categorical ring structures.
Findings
Introduction of 2-modules over symmetric Picard categories
Establishment of foundational definitions and results
Work in progress towards a comprehensive theory
Abstract
Categorical rings were introduced by Jibladze and Pirashvili in their paper "Third Mac Lane cohomology via categorical rings", Journal of Homotopy and related structures, 2, 2007, 187-216. We call those "2-rings". In these notes we present basic definitions and results regarding 2-modules. This is work in progress.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications