Homotopical Aspects of Commutative Algebras I: Freeness Conditions for Crossed Squares
Z. Arvasi, E. Ulualan
TL;DR
This paper provides a new description of the top algebra of free crossed squares of commutative algebras, using tensors and coproducts of crossed modules, enhancing understanding of their homotopical properties.
Contribution
It introduces an alternative formulation of the top algebra of free crossed squares in terms of tensors and coproducts, offering new insights into their structure.
Findings
New description of the top algebra using tensors and coproducts
Enhanced understanding of homotopical properties of crossed squares
Framework for further algebraic and homotopical analysis
Abstract
We give an alternative description of the top algebra of the free crossed square of algebras on 2-construction data in terms of tensors and coproducts of crossed modules of commutative algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology