English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

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