(2,1)-sheaf (changes) in nLab
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Context
Locality and descent
2-Category theory
Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
(∞,1)(\infty,1)-Topos Theory
Contents
Idea
A (2,1)(2,1)-sheaf is a sheaf with values in groupoids. This is traditionally called a stack.
Definition
Let CC be a (2,1)-site. Write Grpd for the (2,1)-category of groupoids, functors and natural isomorphisms.
A (2,1)(2,1)-sheaf on CC is equivalently
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a 2-functor C op→GrpdC^{op} \to Grpd that satisfies descent;
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a 1-truncated (∞,1)-sheaf on CC.
The (2,1)(2,1)-category of (2,1)(2,1)-sheaves
The (2,1)-category of a (2,1)(2,1)-sheaves on a (2,1)-site forms a (2,1)-topos.
There are model category presentations of this (2,1)(2,1)-topos. See model structure for (2,1)-sheaves.
homotopy level n-truncation homotopy theory higher category theory higher topos theory homotopy type theory h-level 0 (-2)-truncated contractible space (-2)-groupoid true/unit type/contractible type h-level 1 (-1)-truncated contractible-if-inhabited (-1)-groupoid/truth value (0,1)-sheaf/ideal mere proposition/h-proposition h-level 2 0-truncated homotopy 0-type 0-groupoid/set sheaf h-set h-level 3 1-truncated homotopy 1-type 1-groupoid/groupoid (2,1)-sheaf/stack h-groupoid h-level 4 2-truncated homotopy 2-type 2-groupoid (3,1)-sheaf/2-stack h-2-groupoid h-level 5 3-truncated homotopy 3-type 3-groupoid (4,1)-sheaf/3-stack h-3-groupoid h-level n+2n+2 nn-truncated homotopy n-type n-groupoid (n+1,1)-sheaf/n-stack h-nn-groupoid h-level ∞\infty untruncated homotopy type ∞-groupoid (∞,1)-sheaf/∞-stack h-∞\infty-groupoid
Last revised on April 25, 2013 at 22:00:22. See the history of this page for a list of all contributions to it.