nLab
hom-connection

hom-connections were introduced in

• Tomasz Brzeziński, Non-commutative connections of the second kind, J. Algebra Appl. 7 (2008), no. 5, 557–-573, MR2009m:58017, arxiv/0802.0445, doi

Later articles

• Tomasz Brzeziński, Laiachi El Kaoutit, Christian Lomp. Non-commutative integral forms and twisted multi-derivations, J. Noncomm. Geom. 4, n. 2, 2010, 281–-312, doi arxiv/0901.2710 MR2011g:58006

• Tomasz Brzeziński, Divergences on projective modules and non-commutative integrals, arxiv/1010.1470

• Serkan Karaçuha, Christian Lomp, Integral calculus on quantum exterior algebras, arxiv/1302.5216