nLab (infinity,1)-presheaf

Context

$(\infty,1)$-Category theory

(∞,1)-category theory

Models

$(\infty,1)$-Topos Theory

(∞,1)-topos theory

Constructions

structures in a cohesive (∞,1)-topos

Contents

Definition

Write $(\infty,0)Cat$ for the category ∞Grpd of $\infty$-groupoids regarded as an (∞,1)-category.

Let $S$ be a simplicial set (which in particular may be a quasi-category).

An $(\infty,1)$-presheaf on $S$ is an (∞,1)-functor

$F : S^{op} \to (\infty,0)Cat \,.$

The (∞,1)-category of $(\infty,1)$-presheaves is the corresponding (∞,1)-category of (∞,1)-functors

$PSh(S) := Fun(S^{op}, (\infty,0)Cat) \,.$

References

Section 5.1 of

Revised on February 4, 2015 19:59:28 by Adeel Khan (77.9.215.246)