Geometric higher groupoids and categories

TL;DR

This paper explores the structure of higher groupoids and categories within an enriched framework, demonstrating their formation as categories of fibrant objects and connecting differential graded algebra nerves to higher categories in algebraic varieties.

Contribution

It introduces a novel perspective on higher categories and groupoids as fibrant objects and links differential graded algebra nerves to higher categories in algebraic geometry.

Findings

Higher groupoids and categories form categories of fibrant objects.

Nerves of differential graded algebras are higher categories in algebraic varieties.

Covers are defined as smooth epimorphisms.

Abstract

In an enriched setting, we show that higher groupoids and higher categories form categories of fibrant objects. The nerve of a differential graded algebra is a higher category in the category of algebraic varieties, where covers are defined to be smooth epimorphisms.