Geodesic
Monoidal functor categories and graphic Fourier transforms
Theory and applications of categories, Tome 25 (2011), pp. 118-141

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This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures. There is a close resemblance to convolution products and the Wiener algebra (of transforms) in functional analysis. The analysis term ``kernel'' (of a distribution) has also been adapted below in connection with certain special types of ``distributors'' (in the terminology of J. Benabou) or ``modules'' (in the terminology of R. Street) in category theory. In using the term ``graphic'', in a very broad sense, we are clearly distinguishing the categorical methods employed in this article from standard Fourier and wavelet mathematics. The term ``graphic'' also applies to promultiplicative graphs, and related concepts, which can feature prominently in the theory.

Publié le :
Classification : 18D10, 18A25
Keywords: monoidal category, promonoidal category, convolution, Fourier transform 
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     author = {Brian J. Day},
     title = {Monoidal functor categories and graphic {Fourier} transforms},
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Brian J. Day. Monoidal functor categories and graphic Fourier transforms. Theory and applications of categories, Tome 25 (2011), pp. 118-141. http://geodesic.mathdoc.fr/item/TAC_2011_25_a4/