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arXiv · 1510.07133

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

İ. İlker Akça·Kadir Emir·João Faria Martins
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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.

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BibTeXRIS

İ. İlker Akça, Kadir Emir, João Faria Martins. 2015-10-24. Two-Fold Homotopy of 2-Crossed Module Maps of Commutative Algebras. https://doi.org/10.1080/00927872.2018.1476523

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