nLab
local section

Contents

Idea

For EXE \to X a bundle, (often taken to be a fiber bundle or at least typically taken to be a regular epimorphic map) a local section is a section of the pullback of the bundle along some UXU \to X, typically required to be an element of a covering family from some coverage.

The assignment of local sections of some EXE \to X to all admissible UXU \to X is the (pre-)sheaf of local sections assigned to a bundle.

In a finitely complete site (S,J)(S,J) the assignment X{p:YX|pX \mapsto \{p\colon Y \to X | p admits local sections over a JJ-cover }\} is a singleton pretopology on SS.

Revised on September 2, 2013 02:09:06 by Todd Trimble (67.81.92.234)