Path space connections and categorical geometry
  We study a type of connection forms, given by Chen integrals, over pathspaces by placing such forms within a category-theoretic framework of principal bundles and connections. We introduce a notion of 'decorated' principal bundles, develop parallel transport on such bundles, and explore specific examples in the context of pathspaces. 
Saikat Chatterjee, Amitabha Lahiri, Ambar N. Sengupta
math.CT math.DG