Akça, İİ, Emir, K and Faria Martins, J orcid.org/0000-0001-8113-3646 (2019) Two-Fold Homotopy of 2-Crossed Module Maps of Commutative Algebras. Communications in Algebra, 47 (1). pp. 289-311. ISSN 0092-7872
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2018 Taylor & Francis Group, LLC. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 07/01/2019, available online: https://doi.org/10.1080/00927872.2018.1476523. |
Keywords: | math.CT; math.CT; math.AT; 55U10 (principal), 18D05, 18D20, 55Q15 (secondary) |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Jun 2018 11:00 |
Last Modified: | 05 Dec 2019 01:38 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/00927872.2018.1476523 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132065 |