Taking categories seriously.

*(English)*Zbl 0648.18001F. W. Lawvere, one of the prophets of category theory, is showing how the elementary concepts of category theory cover very sophisticated notions in mathematics and how their recognition improves the understanding of the corresponding mathematical situations. Special attention is devoted to dynamical systems, which are shown to be closely related to the famous Kan construction. Pursuing his investigations, the author shows how the consideration of enriched category theory and in particular that of the Cauchy completion in that context gives information on questions like convex hull, geodesic distance, and so on.

This paper is to be recommended to the wide public of those people interested in understanding unexpected relations between apparently distant areas of mathematics. And it should definitely be read by those working on category theory or dynamical systems.

This paper is to be recommended to the wide public of those people interested in understanding unexpected relations between apparently distant areas of mathematics. And it should definitely be read by those working on category theory or dynamical systems.

Reviewer: F.Borceux

##### MSC:

18-02 | Research exposition (monographs, survey articles) pertaining to category theory |

37-XX | Dynamical systems and ergodic theory |