Simplicial approach to path homology of quivers, marked categories, groups and algebras

Author:

Ivanov Sergei O.1ORCID,Pavutnitskiy Fedor1

Affiliation:

1. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA) Hefangkou Village, Huaibei Town, Huairou District Beijing China

Abstract

AbstractWe develop a generalisation of the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau (GLMY theory) in a general simplicial setting. The new theory includes as particular cases the GLMY theory for path complexes and new homology theories: path homology of categories with a chosen set of morphisms (marked categories) groups with a chosen subset (marked groups) and path Hochschild homology of algebras with chosen vector subspaces (marked algebras). Using our general machinery, we also introduce a new homology theory for quivers that we call square‐commutative homology of quivers and compare it with the theory developed by Grigor'yan, Muranov, Vershinin and Yau.

Publisher

Wiley

Subject

General Mathematics

Reference24 articles.

1. Magnitude homology and path homology

2. 2019 18th IEEE Int. Conf. Mach. Learn. Appl. (ICMLA);Chowdhury S.,2019

3. Proc. Twenty‐Ninth Ann. ACM‐SIAM Sympos. Discrete Algorithms;Chowdhury S.,2018

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