of our intuitive and naïve understanding that if we ‘stand’ at some point of a path without ‘moving’ along it, then ‘nothing’ must happen with the fibre over that point. This property fixes a 0[-]{}[ary]{} operation in the set of (linear) transports along paths, defining in it the ‘unit’ transport. At last, the equality [[(\[3.1\])]{}]{}, which may be called a group property of the (linear) transports along paths, is a rigorous expression of the intuitive representation that the ‘composition’ of two (linear) transports along one and the same path must be a (linear) transport along the same path.

In general, different forms of [[(\[3.fibre\])]{}]{}–[[(\[3.linear\])]{}]{} are well know properties of the parallel transports generated by (linear) connections (see [@bp-TP-parallelT]). By this reason these transports turn to be special cases of the general (linear) transport along paths [@bp-TP-parallelT theorem 3.1]. In particular, comparing definition \[Defn3.1\] with [@bp-LT-Deriv-tensors definition 2.1] and taking into account [@bp-LT-Deriv-tensors proposition 4.1], we conclude that special types of linear transports along paths are: the parallel transport assigned to a linear connection (covariant differentiation) of the tensor algebra of a manifold , Fermi-Walker transport , Fermi transport [@Synge], Truesdell transport , Jaumann transport , Lie transport , the modified 