New Paper: Cartesian differential storage categories

New Paper: Cartesian differential storage categories

[Robert Seely]

After some delays, the paper "Cartesian differential storage
categories" (Blute-Cockett-Seely) is available on-line, at the ArXiv

    http://arxiv.org/abs/1405.6973

as well as on the third author's webpage

    http://www.math.mcgill.ca/rags/difftl/cart-diff-stor.pdf

The abstact follows:

   Cartesian Differential Storage Categories
    by R. Blute, J.R.B. Cockett, and R.A.G. Seely

Abstract
   Cartesian differential categories were introduced to provide an
   abstract axiomatization of categories of differentiable
   functions. The fundamental example is the category whose objects are
   Euclidean spaces and whose arrows are smooth maps.

   Tensor differential categories provide the framework for categorical
   models of differential linear logic. The coKleisli category of any
   tensor differential category is always a Cartesian differential
   category. Cartesian differential categories, besides arising in this
   manner as coKleisli categories, occur in many different and quite
   independent ways. Thus, it was not obvious how to pass from Cartesian
   differential categories back to tensor differential categories.

   This paper provides natural conditions under which the linear maps of
   a Cartesian differential category form a tensor differential
   category. This is a question of some practical importance as much of
   the machinery of modern differential geometry is based on models
   which implicitly allow such a passage, and thus the results and tools
   of the area tend to freely assume access to this structure.

   The purpose of this paper is to make precise the connection between
   the two types of differential categories. As a prelude to this,
   however, it is convenient to have available a general theory which
   relates the behaviour of "linear" maps in Cartesian categories to the
   structure of Seely categories. The latter were developed to provide
   the categorical semantics for (fragments of) linear logic which use a
   "storage" modality. The general theory of storage, which underlies
   the results mentioned above, is developed in the opening sections of
   the paper and is then applied to the case of differential categories.

-- 
<rags@math.mcgill.ca>
<www.math.mcgill.ca/rags>


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