and much much more….
(…)
Daniel Quillen, Homotopical algebra, Lecture Notes in Mathematics 43, Springer-Verlag 1967, iv+156 pp.
J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995), no. 2, 251–289, MR96c:19002, doi; Cyclic homology and nonsingularity, J. Amer. Math. Soc. 8 (1995), no. 2, 373–442, MR96e:19004, doi