Hi, My paper \bibitem[Bro70]{B70} Brown, R. \newblock \enquote{Fibrations of groupoids}. \newblock \emph{J. Algebra} \textbf{15} (1970) 103--132. gives the preservation of fibrations by pullbacks as Proposition 2.8. You could also look at Heath, P. R. An introduction to homotopy theory via groupoids and universal constructions, Queen’s papers in pure and applied mathematics, Volume 49. Queen’s University, Kingston, Ont. (1978). Ronnie ----Original message----
From : baez@math.ucr.edu Date : 12/03/2017 - 21:23 (GMTST) To : categories@mta.ca Subject : categories: Fibrations of groupoids
Dear Category Theorists - My grad student Kenny Courser is looking for the references where it was first shown that: 1) Fibrations of groupoids are preserved by strict pullbacks. 2) For any functor between groupoids f: G -> H, we can find an equivalence of groupoids g: G -> G' and a fibration f': G' -> H such that f and f'g are naturally isomorphic. If anyone could point us in the right direction, it would be greatly appreciated. Of course these claims may have first been shown in greater generality, and that would be fine too. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]