Adjunction in 2-categories

TL;DR

This paper reviews 2-category theory, focusing on adjunctions, and introduces constructions of derived Morita and Fourier-Mukai 2-categories, demonstrating their embedding over a Noetherian ring.

Contribution

It connects Segal-type and standard approaches to 2-categories and constructs new 2-categories with embedding results over rings.

Findings

Constructed derived Morita 2-category over a Noetherian ring

Constructed Fourier-Mukai 2-category over a Noetherian ring

Embedded one 2-category into the other

Abstract

We give an overview of the parts of arXiv:2004.04279 that deal with 2-categories, up to and including adjunction, and explain how the Segal-type approach to 2-categories adopted there is related to the more standard approaches. As an application, we construct the derived Morita and the Fourier-Mukai 2-categories over a Noetherian ring, and show how to embed one into the other.