On the axiomatization of "parallel transports" and and one its generalization

Abstract

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.