nLab
support

Idea

The term “support” means different things in different parts of mathematics:

In analysis and cohomology

Given $f : X \to A$ some quantity (a function or more generally some cocycle) and for $A$ a pointed object with the point playing the role of a zero element, the support of $f$ is the subobject of $X$ on which $f$ is non-zero.

In topos theory and type theory

support = (-1)-truncation

Related concepts

• compact support

• compactly supported cohomology

• split support