منابع مشابه
Differential categories
Following work of Ehrhard and Regnier, we introduce the notion of a differential category: an additive symmetric monoidal category with a comonad (a " coalgebra modality ") and a differential combinator, satisfying a number of coherence conditions. In such a category, one should imagine the morphisms in the base category as being linear maps and the morphisms in the coKleisli category as being ...
متن کاملCartesian differential categories
This paper revisits the authors’ notion of a differential category from a different perspective. A differential category is an additive symmetric monoidal category with a comonad (a “coalgebra modality”) and a differential combinator. The morphisms of a differential category should be thought of as the linear maps; the differentiable or smooth maps would then be morphisms of the coKleisli categ...
متن کاملDifferential Tannakian categories
We define a differential Tannakian category and show that under a natural assumption it has a fibre functor. If in addition this category is neutral, that is, the target category for the fibre functor are finite dimensional vector spaces over the base field, then it is equivalent to the category of representations of a (pro-)linear differential algebraic group. Our treatment of the problem is v...
متن کاملOn Differential Graded Categories
Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, . . . , Toën and Toën-Vaquié.
متن کاملCartesian Differential Storage Categories
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. Monoidal differential categories provide the framework for categorical models of differential linear logic. The coKleisli category of any monoidal differenti...
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ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 2006
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129506005676