Colax Reedy diagrams

TL;DR

This paper develops a Reedy-style model structure for Segal M-precategories within a symmetric monoidal model category M, extending classical Reedy diagram techniques to non-cartesian monoidal contexts.

Contribution

It introduces a new Reedy model structure for Segal M-precategories in non-cartesian monoidal categories, generalizing classical Reedy diagram methods.

Findings

Established a Reedy model structure for Segal M-precategories

Extended Reedy diagram techniques to non-cartesian monoidal categories

Generalized classical Reedy model structures

Abstract

We use a theory of colax Reedy diagrams to show that the category of Segal M-precategories with fixed set of objects has a model structure for a symmetric monoidal model category M = (M,\otimes,I). What is relevant here is when M is monoidal for a non-cartesian product. The model structure is of Reedy style and generalizes the Reedy model structure for classical Segal M-precategories when M is monoidal for the cartesian product. The techniques we use also generalize the Reedy model structure for classical Reedy diagrams.