nLab Thomason-type model structure

Idea

Thomason-type model categories provide simple 1-categorical models for (∞,1)-categorical objects.

The provide a particularly convenient setting for results like Quillen’s Theorem A? and Theorem B?.

Examples

(∞,1)-categorical structure	1-categorical structure	model structure
∞-groupoid	category	Thomason model structure
∞-groupoid	poset	model structure on posets?
∞-groupoid	2-category	Thomason model structure on 2-categories?
(∞,1)-category	relative category	Barwick–Kan model structure?
connective spectra	symmetric multicategory	Fuentes-Keuthan model structure?
connective spectra	symmetric monoidal groupoid	(only a relative category)
connective spectra	symmetric monoidal category	(only a relative category)

Related concepts

• Thomason model structure

References

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