nLab (2,1)-sheaf



Locality and descent

2-Category theory

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

(∞,1)-topos theory

structures in a cohesive (∞,1)-topos



A (2,1)(2,1)-sheaf is a sheaf with values in groupoids. This is traditionally called a stack.


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

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 leveln-truncationhomotopy theoryhigher category theoryhigher topos theoryhomotopy type theory
h-level 0(-2)-truncatedcontractible space(-2)-groupoidtrue/​unit type/​contractible type
h-level 1(-1)-truncatedcontractible-if-inhabited(-1)-groupoid/​truth value(0,1)-sheaf/​idealmere proposition/​h-proposition
h-level 20-truncatedhomotopy 0-type0-groupoid/​setsheafh-set
h-level 31-truncatedhomotopy 1-type1-groupoid/​groupoid(2,1)-sheaf/​stackh-groupoid
h-level 42-truncatedhomotopy 2-type2-groupoid(3,1)-sheaf/​2-stackh-2-groupoid
h-level 53-truncatedhomotopy 3-type3-groupoid(4,1)-sheaf/​3-stackh-3-groupoid
h-level n+2n+2nn-truncatedhomotopy n-typen-groupoid(n+1,1)-sheaf/​n-stackh-nn-groupoid
h-level \inftyuntruncatedhomotopy type∞-groupoid(∞,1)-sheaf/​∞-stackh-\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.