Modules over invertible 1-cocycles
Jos\'e Manuel Fern\'andez Vilaboa, Ram\'on Gonz\'alez Rodr\'iguez,, Brais Ramos P\'erez, Ana Bel\'en Rodr\'iguez Raposo
TL;DR
This paper introduces a new concept of modules over invertible 1-cocycles within braided categories and establishes categorical equivalences with modules over Hopf braces, advancing the understanding of algebraic structures in this setting.
Contribution
It defines left modules over invertible 1-cocycles in braided categories and proves their categorical equivalence with modules over Hopf braces, providing new insights into these algebraic frameworks.
Findings
Established categorical equivalences between modules over invertible 1-cocycles and Hopf braces.
Extended module theory to braided settings for invertible 1-cocycles.
Provided foundational results linking algebraic structures in braided categories.
Abstract
In this paper we introduce in a braided setting the notion of left module for an invertible 1-cocycle and we prove some categorical equivalences between categories of modules associated to an invertible 1-cocycle and categories of modules associated to Hopf braces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Advanced Topics in Algebra