On the axiomatization of "parallel transports" and and one its   generalization
  A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel transports. Some properties of the general transports along paths are presented. 
Bozhidar Z. Iliev (Institute for Nuclear Research and Nuclear Energy,   Bulgarian Academy of Sciences, Sofia, Bulgaria)