Artin's criteria for algebraicity revisited

TL;DR

This paper revisits Artin's algebraicity criteria for functors and groupoids, providing new proofs using homogeneity notions that unify and generalize previous theorems.

Contribution

It introduces a more general framework that unifies Artin's two main theorems and clarifies their differences through homogeneity concepts.

Findings

New proofs of Artin's algebraicity criteria

A unified approach to Artin's theorems

Clarification of differences between theorems

Abstract

Using notions of homogeneity we give new proofs of M. Artin's algebraicity criteria for functors and groupoids. Our methods give a more general result, unifying Artin's two theorems and clarifying their differences.