Cyclic homology of exact categories: Keller
Baues and Muro, see page 118. See perhaps also other things by Baues, e.g. Combinatorial foundations book.
A note by May on Grothendieck rings and Picard groups, and another note on caterads. See also http://www.math.uiuc.edu/K-theory/0409 and http://www.math.uiuc.edu/K-theory/0474.
Possibly of some interest: Nenashev, Garkusha, Davis and Lueck
Ulbrich: On cohomology of graded group categories. Compositio Mathematica, 63 no. 3 (1987)
nLab page on Cohomology in categories