| J. B enabou, Categories avec multiplication, C. R. Acad. Sci. Paris 256, 63, 1887-1890. 35 |
....and Computer science, University of Leicester, University road, Leicester LE1 7RH, England e mail: vs27 mcs.le.ac.uk 1 objects respectively of V Cat and W Cat. The rst point of our problem was answered in [KLSS99] Let us start from the de nition of monoidal functor between monoidal categories [Ben63] and enrichments over them [EiKe66] Law73] A monoidal functor F : V W induces a 2 functor F : V Cat W Cat. MonCat is equipped with a 2 categorical structure by de ning 2 cells in it as monoidal natural transformations ( EiKe66] The process ( of sending V to V Cat and F to F extends ....
J. B enabou, Categories avec multiplication, C. R. Acad. Sci. Paris 256, 63, 1887-1890. 35
....theory, both treated extensively in [CWM] One of these is the notion of a monad or triple on a category, which goes back to Godement [G] and was rst developed by Eilenberg, Moore, Beck and others. The other is that of a monoidal category or tensor category, which originates with B enabou [B e] and with Mac Lane s famous coherence theorem [MacL] and which pervades much of present day mathematics. For a monad S on a tensor category, there is a natural additional structure that one can impose, namely that of a comparison map S(X 1 Xn ) S(X 1 ) S(Xn ) n 0) ....
J. Benabou, Categories avec multiplication, C.R. Acad. Sci. Paris 256 (1963), 1887-1890.
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