Categories for Me, and You?

TL;DR

This paper provides notes on category theory concepts such as locally cartesian closed categories and structures in slice and Eilenberg-Moore categories, including references and proofs, some of which are new.

Contribution

It offers a collection of notes with references and proofs on advanced category theory topics, some of which are presented for the first time.

Findings

Definitions and properties of locally cartesian closed categories

Descriptions of cartesian structures in slice categories

Pseudo-cartesian structures on Eilenberg-Moore categories

Abstract

A non-self-contained gathering of notes on category theory, including the definition of locally cartesian closed category, of the cartesian structure in slice categories, or of the pseudo-cartesian structure on Eilenberg-Moore categories. References and proofs are provided, sometimes, to my knowledge, for the first time.