nLab chaos

Contents

Idea

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According to Lawvere 1984, codiscrete objects, i.e. those in the image of a right adjoint to a forgetful functor, may be though of as “chaotic” with repect to whatever mathematical structure was forgotten by the forgetful functor.

This convention matches/subsumes more-or-less common terminology such as chaotic topology or chaotic groupoid.

The terminology “chaotic” for codiscrete objects goes back to

where it is used for Grothendieck topologies, from which it was, apparently, adapted to chaotic topologies on topological spaces.

General formalization of the concept in terms of right adjoints to forgetful functors is due to:

William Lawvere, Functorial Remarks on the General Concept of Chaos, IMA Preprint 87, 1984 (pdf)

Last revised on August 25, 2021 at 19:56:24. See the history of this page for a list of all contributions to it.