  In the first part of this paper we show that path categories are enriched
over groupoids, in a way that is compatible with a suitable 2-category of path
categories. In the second part we introduce a new notion of homotopy
exponential and homotopy Pi-type for path categories, the strong homotopy
exponential and the strong homotopy Pi-type. We prove some of their basic
properties, along with two important technical propositions. The results in the
second part of this paper are mostly obtained using the groupoid enrichment of
path categories established in the first part.
