nLab
representable morphism of stacks
Contents
Context
-Topos Theory
(∞,1)-topos theory
Background
Definitions
-
elementary (∞,1)-topos
-
(∞,1)-site
-
reflective sub-(∞,1)-category
-
(∞,1)-category of (∞,1)-sheaves
-
(∞,1)-topos
-
(n,1)-topos, n-topos
-
(∞,1)-quasitopos
-
(∞,2)-topos
-
(∞,n)-topos
Characterization
Morphisms
Extra stuff, structure and property
-
hypercomplete (∞,1)-topos
-
over-(∞,1)-topos
-
n-localic (∞,1)-topos
-
locally n-connected (n,1)-topos
-
structured (∞,1)-topos
-
locally ∞-connected (∞,1)-topos, ∞-connected (∞,1)-topos
-
local (∞,1)-topos
-
cohesive (∞,1)-topos
Models
Constructions
structures in a cohesive (∞,1)-topos
Contents
Definition
A morphism of stacks over a site is called representable if for all representable objects and all morphisms the homotopy pullback in
is again representable.
Properties
Push-forward in generalized cohomology
Along representable morphisms of stacks over smooth manifolds (smooth infinity-groupoids) is induced a push-forward in generalized cohomology operation.
References
The general definition appears for instance as def. 38.5 in
(there with stacks perceived equivalently and dually under the Grothendieck construction as fibered categories).
Applications of push-forward in generalized cohomology along representable morphisms appear for instance in
Last revised on November 7, 2012 at 21:53:48.
See the history of this page for a list of all contributions to it.