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.) 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:
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Presheaf of spaces Wikipedia(Text) CC BY-SA