Minimal accessible categories
Ji\v{r}\'i Rosick\'y
TL;DR
This paper provides a category-theoretic proof that the category of linearly ordered sets with order-preserving injections is minimally finitely accessible, and discusses the existence of a minimal -accessible category.
Contribution
It offers a new purely category-theoretic proof of a known minimality result and explores the existence of minimal -accessible categories.
Findings
Category of linearly ordered sets is minimally finitely accessible.
Provides a purely category-theoretic proof of Makkai and Pare9's result.
Discusses the potential existence of a minimal -accessible category.
Abstract
We give a purely category-theoretic proof of the result of Makkai and Par\'e saying that the category of linearly ordered sets and order preserving injective mappings is a minimal finitely accessible category. We also discuss the existence of a minimal -accessible category.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Fuzzy and Soft Set Theory