nLab
(infinity,1)-category of cartesian sections

Idea

Let p:EXp : E \to X be an (∞,1)-functor of (∞,1)-categories. A cartesian section of pp is a section σ:XE\sigma : X \to E that sends all 1-morphisms in XX to Cartesian morphisms in EE.

Definition

Remarks

If p:EXp : E \to X is a Cartesian fibration classified by an (∞,1)-functor F:X(,1)Cat opF : X \to (\infty,1)Cat^{op} then Γ X cart(E)\Gamma_X^{cart}(E) is equivalent to the limit of FF

Γ X cart(E)limF. \Gamma_X^{cart}(E) \simeq lim F \,.

See the discussion at limit in a quasi-category for details.

Refernces

In corollary 3.3.3.2 of

the collection of cartesian sections of p:EXp : E \to X appears as Maps X (X #,E cart)Maps_X^\flat(X^#, E^{cart}).

Here

Created on August 12, 2009 22:29:22 by Urs Schreiber (88.128.80.173)