Cartesian differential categories revisited
Author:
- 13 April 2015
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Structures in Computer Science
- Vol. 27 (1) , 70-91
Abstract
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 categories with finite products, so that every category with finite products 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.Keywords
All Related Versions
This publication has 9 references indexed in Scilit:
- Differential Structure, Tangent Structure, and SDGApplied Categorical Structures, 2013
- Constructing differential categories and deconstructing categories of gamesInformation and Computation, 2013
- What is a categorical model of the differential and the resource λ-calculi?Mathematical Structures in Computer Science, 2012
- Restriction categories III: colimits, partial limits and extensivityMathematical Structures in Computer Science, 2007
- Differential categoriesMathematical Structures in Computer Science, 2006
- Synthetic Differential Geometry2006
- The differential lambda-calculusTheoretical Computer Science, 2003
- Restriction categories I: categories of partial mapsTheoretical Computer Science, 2002
- Categories of partial mapsInformation and Computation, 1988