Let A be an augmented algebra then Hoch(A,k) \iso Ext_A(k,k) where k is the target of the augmentation can be computed as the cohomology of Hom_k(BA,A) so the Gerstenhaber cup product is the Yoneda product is the product induced from the ususal diagonal on BA BUT where in the literature is this ever discussed?? jim +++++++++++++++++++++++++++++++++
The identification of Hoch(A,k) with Ext_A(k,k) is pretty thoroughly aired in Cartan-Eilenberg, but you must know that already. As for the cup product coming from the diagonal, that may be in one of Murray's original deformation papers. I think Eilenberg mentioned it in passing in his homological algebra course (which all instructors at Columbia were expected to sit in on, at least if they were in algebra or topology). But if I had to search the literature, I think I would start with the work of Steenrod. As for categories, I must admit to total ignorance. Michael ===========================
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barr＠triples.Math.McGill.CA -
James Stasheff