Presentations of Grothendieck constructions

TL;DR

This paper provides quiver presentations for Grothendieck constructions of functors from small categories to the 2-category of a0a0a0-categories, enhancing understanding of their algebraic structure.

Contribution

It introduces explicit quiver presentations for Grothendieck constructions in the context of a0-categories, offering a new algebraic perspective.

Findings

Provides explicit quiver descriptions

Facilitates algebraic analysis of Grothendieck constructions

Enhances understanding of categorical structures

Abstract

We will give quiver presentations of the Grothendieck constructions of functors from a small category to the 2-category of $\Bbbk$-categories for a commutative ring $\Bbbk$.