nLab
(infinity,1)-presheaf

Context

(,1)(\infty,1)-Category theory

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Definition

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

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

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

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

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

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

Remarks

References

Section 5.1 of

Revised on June 28, 2013 01:06:18 by Urs Schreiber (80.90.61.2)