A sufficient criterion for homotopy cartesianess
Alberto Canonaco, Matthias Kuenzer
TL;DR
This paper establishes a new criterion for identifying homotopy cartesian squares in Verdier triangulated categories, based on cone isomorphisms and finiteness conditions on endomorphism rings.
Contribution
It introduces a sufficient condition for a commutative quadrangle to be homotopy cartesian, linking cone isomorphisms with finiteness assumptions.
Findings
Provides a criterion for homotopy cartesian quadrangles
Connects cone isomorphisms with endomorphism ring conditions
Advances understanding of triangulated category structures
Abstract
Suppose given a commutative quadrangle in a Verdier triangulated category such that there exists an induced isomorphism on the horizontally taken cones. Suppose that the endomorphism ring of the initial or the terminal corner object of this quadrangle satisfies a finiteness condition. Then this quadrangle is homotopy cartesian.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models