Historical question: who first formulated the notion of "equivalence of categories"?
It's not in Eilenberg-Mac Lane's 1945 paper. The earliest formulation I can find is in Grothendieck's Tohoku paper (1957), where he defines it immediately after functor and natural transformation.
Also Dold in "Symmetric Products ..." (1958). He doesn't quite state it as a general notion, but it is clear he knows it and that the theorem he's proving about chain complexes and simplicial abelian groups is an example.
What's a good reference for homotopical approach to spaces of embeddings of manifolds? I'm interested in whether new technologies like factorization homology have already been applied to this area.
