Fibrancy of Partial Model Categories

TL;DR

This paper explores fibrancy conditions in the Thomason model structure, demonstrating that weak equivalences in partial model categories are fibrant and linking these concepts to calculi of fractions.

Contribution

It establishes that the category of weak equivalences in a partial model category is fibrant and connects fibrancy conditions to calculi of fractions.

Findings

Weak equivalences form fibrant categories in partial model categories.

Connections between fibrancy and calculi of fractions are established.

Provides insights into fibrancy conditions in the Thomason model structure.

Abstract

We investigate fibrancy conditions in the Thomason model structure on the category of small categories. In particular, we show that the category of weak equivalences of a partial model category is fibrant. Furthermore, we describe connections to calculi of fractions.