Connections in Tangent Categories
arXiv:1610.08774
Abstract
Connections are an important tool of differential geometry. This paper investigates their definition and structure in the abstract setting of tangent categories. At this level of abstraction we derive several classically important results about connections, including the Bianchi identities, identities for curvature and torsion, almost complex structure, and parallel transport.
This version fixes a number of typos and small errors in an earlier version. To be published in Theory and Applications of Categories