nLab critical point

Context

Differential geometry

differential geometry

synthetic differential geometry

Contents

Definition

For $f : X \to Y$ a smooth function, a critical point is a point $x \in X$ at which the derivative $d X : T X \to T Y$ vanishes.

The collection of all critical points is also called the critical locus of $f$.

A formalization of this in cohesive geometry is at cohesive (infinity,1)-topos – infinitesimal cohesion – critical locus.

Applications

Revised on April 21, 2014 06:29:57 by Mike Shulman (108.247.151.163)