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2012

Cartesian differential categories revisited

Cruttwell, G. S. H.

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We revisit the definition of Cartesian differential categories, showing that a slightly more general version is useful for a number of reasons.

As one application, we show that these general differential categories are comonadic over Cartesian categories, so that every Cartesian category has an associated cofree differential category.
We also work out the corresponding results when the categories involved have restriction structure, and show that these categories are closed under splitting restriction idempotents.

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Rosický, J. Abstract tangent functors. Diagrammes , 12, Exp. No. 3, 1984
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Cockett, R. and Lack, S. Restriction categories I: categories of partial maps. Theoretical computer science , 270
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Ehrhard, T., and Regnier, L. The differential lambda-calculus. Theoretical Computer Science , 309
2003
Earlier work this paper cites.
Kock, A. Synthetic Differential Geometry , Cambridge University Press (2nd ed.). Also available at http://home.imf.au.dk/kock/sdg99.pdf, 2006
2006
Earlier work this paper cites.

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Then

Cockett, R.. “Can you differentiate a polynomial?”, talk given at FMCS 2012; available online at http://www.mscs.dal.ca/ selinger/fmcs2012/slides/FMCS2012-Cockett2.pdf
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