Classifying global dimensions of category algebras of some finite combinational categories

TL;DR

This paper classifies the global dimensions of category algebras associated with various finite combinatorial categories, extending understanding of their homological properties.

Contribution

It provides a comprehensive classification of global dimensions for category algebras of several finite combinatorial categories, including truncations of well-studied categories.

Findings

Global dimensions are explicitly classified for each category.

Results extend known homological properties of these categories.

Provides a foundation for further algebraic and homological investigations.

Abstract

In this paper we classify global dimensions of the category algebras of some finite categories, including finite truncations of the categories $FI$, $FI_G$, $FI_d$, $OI$, $OI_G$, $OI_d$ and $VI$