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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove that the global dimension of the complex algebra of the monoid ofall partial functions on an n-set is $n-1$ for all $n\geq 1$. This is also theglobal dimension of the complex algebra of the category of all epimorphismsbetween subsets of an $n$-set. In our proof we use standard homological methodsas well as combinatorial techniques associated to the representation theory ofthe symmetric group. As part of the proof, we obtain a partial description ofthe Cartan matrix of these algebras.

The global dimension of the algebra of the monoid of all partial  functions on an $n$-set as the algebra of the EI-category of epimorphisms  between subsets