Monoidal Pull-Push I: Cocartesian Fibrations and Categories of Spans

TL;DR

This paper develops a theory of cocartesian fibrations between Segal spaces and uses it to prove a theorem of Barwick, advancing the categorical understanding of spans and fibrations.

Contribution

It introduces a foundational framework for cocartesian fibrations between Segal spaces and applies it to prove a significant existing theorem in higher category theory.

Findings

Established a basic theory of cocartesian fibrations between Segal spaces

Provided a new proof of Barwick's theorem from 2014

Enhanced the categorical understanding of spans and fibrations

Abstract

We develop a basic theory of cocartesian fibrations between Segal spaces (in line with that of arxiv:2102.05190), and use it to provide a proof of a theorem of Barwick (the main result of arxiv:1404.0108). Note: This work was originally the author's master's thesis, submitted 21.09.2020.