Homotopy Theory of T-algebras over Top-Cat ?

TL;DR

This paper explores the interplay between infinity categories and 2-categories by constructing a path object in topological categories, developing a 2-monad for monoidal topological categories, and relating these to T-algebras.

Contribution

It introduces an explicit functorial path object in topological categories and constructs a 2-monad for symmetric monoidal topological categories, linking higher category theories.

Findings

Constructed a functorial path object in topological categories

Developed a 2-monad for symmetric monoidal topological categories

Connected the theory to the model structure on T-algebras

Abstract

In this article, we interconnect two different aspects of higher category theory, in one hand the theory of infinity categories and on an other hand the theory of 2-categories.We construct an explicit functorial path objet in the model category of topological categories. We discuss some properties and consequences of such path object. We also explain the construction of a 2-monad which algebras are (symmetric) monoidal topological categories. Finally, we explain the relationship with the eventual model structure on the category of T-algebras.