Geoff Cruttwell (Ottawa, Canada), Reconsidering Cartesian differential categories
Schedule
- Feb. 24, 2012, 11:20 - 12:00
Abstract
(joint work with Robin Cockett)
Blute, Cockett and Seely defined Cartesian differential categories as a
beginning for the study of the categorical semantics of Ehrhard and Regnier’s
differential λ-calculus. As we shall see, however, several small problems
with the definition mean that it is less robust than desired. For one example,
while smooth maps between Cartesian spaces are an example of a Cartesian
differential category, smooth maps between open subsets of Cartesian spaces
are not.
Through a slight generalization of the definition of Cartesian differential
categories, we shall show that this and other problems can be resolved.
In particular, following work by Cockett and Seely, we will show that
the resulting generalized Cartesian differential categories are comonadic over
cartesian categories, providing a wealth of new examples.
Attachments
(joint work with Robin Cockett)
Blute, Cockett and Seely defined Cartesian differential categories as a beginning for the study of the categorical semantics of Ehrhard and Regnier’s differential λ-calculus. As we shall see, however, several small problems with the definition mean that it is less robust than desired. For one example, while smooth maps between Cartesian spaces are an example of a Cartesian differential category, smooth maps between open subsets of Cartesian spaces are not. Through a slight generalization of the definition of Cartesian differential categories, we shall show that this and other problems can be resolved. In particular, following work by Cockett and Seely, we will show that the resulting generalized Cartesian differential categories are comonadic over cartesian categories, providing a wealth of new examples.