Categories in continuum physics : lectures given at a workshop held at SUNY, Buffalo, 1982 / F. W. Lawvere and S. H. Schanuel

From the introduction (by Lawvere): "The articles collected in this volume reflect talks given at a workshop on Category Theory and the Foundations of Continuum Thermomechanics which was held at SUNY Buffalo in May 1982. The workshop permitted the beginning of more extensive exchange of ideas between groups of researchers which had previously had very little contact. Noll and Williams discuss here the foundations of the theory of material bodies, in particular the current status of Cauchy's stress theorem, while Coleman, Feinberg, Lavine and Owen describe general contexts in which the existence of temperature and entropy have been established for rapidly deforming, unequally heated bodies. In apparently different directions, Chen and Frölicher discuss simplification of the foundation of infinite-dimensional differential geometry, as do Kock and Reyes with special attention to the axiomatics of that subject as a whole and to the variety of useful models of the resulting theory. The geometric theory is necessarily categorical, and I want to indicate in this introduction some of the advantages which may result if the abstract structures arising in thermomechanics are also explicitly recognized as categories.''
Contents: F. William Lawvere, Introduction (pp. 1–16); Walter Noll, Continuum mechanics and geometric integration theory (pp. 17–29); William O. Williams, Structure of continuum physics (pp. 30–37); Kuo Tsai Chen, On differentiable spaces (pp. 38–42); Alfred Frölicher, Cartesian closed categories and analysis of smooth maps (pp. 43–51); Anders Kock, Introduction to synthetic differential geometry, and a synthetic theory of dislocations (pp. 52–68); Gonzalo E. Reyes, Synthetic reasoning and variable sets (pp. 69–82); Bernard D. Coleman and David R. Owen [David Ross Owen], Recent research on the foundations of thermodynamics (pp. 83–99); David R. Owen [David Ross Owen], Global and local versions of the second law of thermodynamics (pp. 100–114); Martin Feinberg and Richard Lavine, Thermodynamics and the Hahn-Banach theorem (pp. 115–117); Stephen H. Schanuel, What is the length of a potato? An introduction to geometric measure theory (pp. 118–126).