Kan extensions along promonoidal functors

Brian Day and Ross Street

Strong promonoidal functors are defined. Left Kan extension (also called "existential quantification") along a strong promonoidal functor is shown to be a strong monoidal functor. A construction for the free monoidal category on a promonoidal category is provided. A Fourier-like transform of presheaves is defined and shown to take convolution product to cartesian product.

Keywords: monoidal functor, promonoidal category, Kan extension, Fourier transform, convolution tensor product.

AMS Classification (1991): 18D10.

Theory and Applications of Categories, Vol. 1, 1995, No. 4, pp 72-78.


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