Two-Fold Homotopy of 2-Crossed Module Maps of Commutative Algebras

We address the homotopy theory of 2-crossed modules of commutative algebras. In particular, we define the concept of a 2-fold homotopy between a pair of 1-fold homotopies connecting 2-crossed module maps \(\A \to \A'\). We also prove that if the domain 2-crossed module \(\A\) is free up to orde...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: İ. lker Akça, adir Emir, oão Faria Martins
Format: Article
Language:English
Subjects:
Algebra
Homotopy theory
Modules
Polynomials
Online Access:Get full text
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Summary:We address the homotopy theory of 2-crossed modules of commutative algebras. In particular, we define the concept of a 2-fold homotopy between a pair of 1-fold homotopies connecting 2-crossed module maps \(\A \to \A'\). We also prove that if the domain 2-crossed module \(\A\) is free up to order one (i.e. if the bottom algebra is a polynomial algebra) then we have a 2-groupoid of 2-crossed module maps \(\A \to \A'\) and their homotopies and 2-fold homotopies.
ISSN:2331-8422
DOI:10.48550/arxiv.1510.07133