Nonabelian Bundle Gerbes from 2-Transport Part I: Synthetic Bibundles Urs Schreiber * December 7, 2005 Abstract It is shown that 1-morphisms between 2-functors from 2-paths to the category BiTor (H) define bibundles with bibundle connection the way they appear in nonabelian bundle gerbes. An arrow theoretic description of bibundle connections is given using synthetic differential geometry. In a sequel to this paper this will be used to show that pre-trivializations of 2-functors to BiTor (H) are in bijection with fake flat nonabelian bundle gerbes. (Unfinished and unscrutinized private draft.) * E-mail: urs.schreiber at math.uni-hamburg.de 1