Theory and Applications of Categories, Vol. 8, 2001.

ADDENDUM: ASPECTS OF FRACTIONAL EXPONENT FUNCTORS

ANDERS KOCK AND GONZALO E. REYES

Concerning the notion and significance of Atoms: We found and utilized in [2] that the exponential functors like (−)^{D} preserve colimits; Lawvere then pointed out (in Toward the description in a Smooth Topos of the Dynamically Possible Motions and Deformations of a Continuous Body, Cahiers de Topologie et Géométrie Différentielle Catégoriques XXI (1980), 337-392) that this implies the existence of right adjoints for them, and that these right adjoints deserve study. See also Toposes of Laws of Motion , Transcript of video of invited talk at AMS Meeting 924, Montreal, September 1997, (pdf)

http://www.acsu.buffalo.edu/ wlawvere

References

[1] A. Kock and G.E. Reyes, Aspects of fractional exponent functors, Theory and Applications of Categories 5 (1999), No. 10, 251–265.

[2] A. Kock and G.E. Reyes, Manifolds in formal differential geometry, in Durham Proceedings 1977, Springer Lecture Notes 753 (1979).

Institut for Matematiske Fag, Aarhus Univ., DK 8000 Aarhus C, Denmark and Dept. de Mathématiques, Univ. de Montréal, Montréal, P.Q., Canada

Email: kock@imf.au.dk and reyes@MATHCN.UMontreal.CA

This article may be accessed via WWW at http://www.tac.mta.ca/tac/ or by anony-

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Received by the editors 2001 January 2.

Published on 2001 February 7.

\begin{matrix}c \\ ◯ \end{matrix} Anders Kock and Gonzalo E. Reyes, 2001. Permission to copy for private use granted.

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