Foundations of a Recent Extension of Category Theory and Topos Theory

TL;DR

This paper introduces generalized category theory concepts used in recent extensions of category and topos theory, focusing on functors, natural transformations, and limits in a broad setting.

Contribution

It provides an accessible overview of generalized category theory foundational to recent advances in extended category and topos theories.

Findings

Clarifies functors, natural transformations, and limits in generalized categories

Summarizes key constructions used in recent extended category theories

Serves as an introductory guide to generalized categorical logic

Abstract

This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural transformations, adjoints, and limits in a generalized setting, giving a concise outline of these frequently arising constructions.