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arXiv · 1411.6931

Pointed Homotopy of Maps Between 2-Crossed Modules 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, which are equivalent to simplicial commutative algebras with Moore complex of length two. In particular, we construct for maps of 2-crossed modules a homotopy relation, and prove that it yields an equivalence relation in very unrestricted cases (freeness up to order one of the domain 2-crossed module). This latter condition strictly includes the case when the domain is cofibrant. Furthermore, we prove that this notion of homotopy yields a groupoid with objects being the 2-crossed module maps between two fixed 2-crossed modules (with free up to order one domain), the morphisms being the homotopies between 2-crossed module maps.

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İ. İlker Akça, Kadir Emir, João Faria Martins. 2014-11-25. Pointed Homotopy of Maps Between 2-Crossed Modules of Commutative Algebras. https://doi.org/10.4310/hha.2016.v18.n1.a6

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