nLab representable morphism of stacks



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

(∞,1)-topos theory

structures in a cohesive (∞,1)-topos



A morphism f:XYf : X \to Y of stacks over a site CC is called representable if for all representable objects UCYStacks(C)U \in C \stackrel{Y}{\hookrightarrow} Stacks(C) and all morphisms UYU \to Y the homotopy pullback X× YUX \times_Y U in

X× YU X f U Y \array{ X \times_Y U &\to& X \\ \downarrow &{}^{\simeq}\swArrow& \downarrow^f \\ U &\to& Y }

is again representable.


Push-forward in generalized cohomology

Along representable morphisms ff of stacks over smooth manifolds (smooth infinity-groupoids) is induced a push-forward in generalized cohomology operation.


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.