nLab (infinity,1)-sheafification

Idea

As for ordinary sheafification, $(\infty,1)$-sheafification is the left exact left adjoint (∞,1)-functor to the inclusion of (∞,1)-sheaves into (∞,1)-presheaves.

For more details see (∞,1)-category of (∞,1)-sheaves.

Properties

An $(n,1)$-presheaf can be $(n,1)$-sheafified by

• applying the plus-construction on presheaves $n+1$ times (see Lurie, section 6.5.3)

• applying a single “hypercover-plus-construction” (see DHI, theorem 7.6)

Related concepts

• sheafification, plus-construction on presheaves

• (∞,1)-sheafification / ∞-stackification

References

The iterated plus-construction is mentioned in section 6.5.3 of

• Jacob Lurie, Higher Topos Theory

The “hypercover-plus construction” is discussed around theorem 7.6 of

• Dan Dugger, Sharon Hollander, Dan Isaksen, Hypercovers and simplicial presheaves (pdf)