Categorical structures in physics (Q1264383)

This paper is a brief exposition of two categories which arise naturally in the mathematical description of physical systems: the category of \({\mathcal M}\)-spaces [\textit{A. Fröhlicher} and \textit{A. Kriegl}, ``Linear spaces and differentiation theory'', Wiley, Chichester (1988; Zbl 0657.46034)], in particular, of smooth spaces, and the category of Hilbert geometries [\textit{Cl.-A. Faure} and \textit{A. Fröhlicher}, Geom. Dedicata 56, No. 3, 225-236 (1995; Zbl 0836.51002)].