Homology theory of multiplicative systems

André Joyal – 11 November 1998

In 1951 Eilenberg and MacLane published their paper "Homology Theories of Multiplicative systems". The paper has remained quite mysterious until the recent work of Teimuraz Pirashvili (Topology 1996) showing that Mac Lane's cubical construction is computing the homology of a left Kan extension. We wish to propose a general interpretation of this discovery. We shall use operads and multilinear categories.