Homotopy cartesian diagrams in n-angulated categories
Zengqiang Lin, Yan Zheng
TL;DR
This paper explores the relationships between key axioms in n-angulated categories, providing new equivalent formulations using homotopy cartesian diagrams to deepen understanding of their structure.
Contribution
It introduces new equivalent statements of the higher mapping cone axiom via homotopy cartesian diagrams, clarifying its connection to the higher octahedral axiom.
Findings
New equivalent statements of the higher mapping cone axiom
Homotopy cartesian diagrams as a tool for understanding n-angulated categories
Enhanced explanation of the higher octahedral axiom
Abstract
It has been proved by Bergh and Thaule that the higher mapping cone axiom is equivalent to the higher octahedral axiom for n-angulated categories. In this note, we use homotopy cartesian diagrams to give several new equivalent statements of the higher mapping cone axiom, which are applied to explain the higher octahedral axiom.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models