Perhaps the closest that Weyl came to discussing things related to categories and functors is in his marvellous address at the 1954 International Congress of Mathematicians when he spoke on the work of the Fields Medal winners, Kodaira and Serre. As cohomology and sheaves featured prominently in their work, as well of course as spectral sequences (at least in Serre's work), his writtren text, according to a footnote more expansive than what he said at the Congress, goes quite far in "explaining" what de Rham cohomology is, what additional structures result when the manifold is a complex or Kahler or Hodge manifold, how there is a great interplay between the analysis of several complex variables, linear partial differential equations, algebraic geometry over the complex numbers, the Hirzebruch Riemann-Roch theorem (which was actually a conjecture of Serre and was, of course, nd generalized by Grothendieck to a relative statement valid over any base field), the Serre duality theorem (discussed by Weyl, only over the complex numbers), the theorems A and B (of Cartan and Serre), Serre's work on homotopy groups, the Serre spectral sequence. the work of Serre together with Hochschild on cohomology of groups and Lie algebras, .... Bill Messing [For admin and other information see: http://www.mta.ca/~cat-dist/ ]