Homology of systemic modules
Jaiung Jun, Kalina Mincheva, Louis Rowen
TL;DR
This paper introduces a tropical homology theory for systemic modules, establishing foundational results like Schanuel's lemma, projective dimension, and a weak Snake lemma within this new framework.
Contribution
It develops the initial framework of tropical homology for systemic modules, including key lemmas and concepts not previously formulated.
Findings
A version of Schanuel's lemma for systemic modules
Definition of projective dimension in tropical homology
Introduction of the homology semi-module and a weak Snake lemma
Abstract
We develop the rudiments of a tropical homology theory, based on "triples" and "systems." Results include a version of Schanuel's lemma, projective dimension, the homology semi-module, and a weak Snake lemma.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models