Notes on some categories related to that of finite totally ordered sets
Takuo Matsuoka
TL;DR
This paper compiles various facts about the category of finite totally ordered sets and related categories, aiming to support the study of iterated meta-theories of algebra within higher order universal algebra.
Contribution
It provides a collection of results on finite totally ordered sets and related categories to facilitate research in higher order algebraic theories.
Findings
Results on the structure of finite totally ordered sets
Properties of related categorical frameworks
Foundational facts for higher order algebraic studies
Abstract
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly meta theories of algebra in the style of our work arXiv:1601.00301 (arXiv:1601.00301), which is a kind of higher order universal algebra.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Logic · Advanced Topology and Set Theory