Presheaf of spaces

In mathematics, a presheaf of spaces on an ∞-category C is a contravariant functor from C to the ∞-category of spaces (for example, the nerve of the category of CW-complexes.)^[1] It is an ∞-category version of a sheaf of sets, as a "set" is replaced by a "space". The notion is used, among other things, in the ∞-category formulation of Yoneda's lemma that says: $C \to PShv(C)$ is fully faithful (here C can be just a simplicial set.)^[2]

References

1. Lurie, Definition 1.2.16.1.
2. Lurie, Proposition 5.1.3.1.

• Lurie, J. Higher Topos Theory