Operads are a useful way of encoding compositions of maps from n variables to 1, modelled on grafting of trees - root to branchtip and as such appear e.g. in ``classical'' closed string field theory Qunatum corrections require a generalization for which the model should be the category of tangles or some such Any work been done on such a generalization? jim stasheff ==============================================================================
Jim Stasheff and a few others have a copy of old 1972 notes of mine on operads, essentially studying, besides the obvious convolution tensor product on the functor category [P,V], another derived one, the monads for which generalize Peter May's operads. Here P is the category of natural numbers and permutations while V is any symmetric monoidal closed category (complete and cocomplete). The case V = Set is familiar from Joyal's species. Suppose we replace P here by the braid category B; everything still seems to work, at a first brief glance; so we have a notion of B-operad. Is this what Jim is asking for? Max Kelly. ==============================================================================
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Dip. Mat. - visitatore -
jds＠rademacher.math.upenn.edu