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A convenient differential category
, 2011
"... We show that the category of convenient vector spaces in the sense of Frölicher ..."
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We show that the category of convenient vector spaces in the sense of Frölicher
An algebraic process calculus
 In Proceedings of the twentythird annual IEEE symposium on logic in computer science (LICS
, 2008
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Cartesian differential storage categories
, 2014
"... 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 cat ..."
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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
Derivations in Codifferential Categories
, 2015
"... Dedication. The authors dedicate this work to the memory of Jim Lambek. Derivations provide a way of transporting ideas from the calculus of manifolds to algebraic settings where there is no sensible notion of limit. In this paper, we consider derivations in certain monoidal categories, called codif ..."
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Dedication. The authors dedicate this work to the memory of Jim Lambek. Derivations provide a way of transporting ideas from the calculus of manifolds to algebraic settings where there is no sensible notion of limit. In this paper, we consider derivations in certain monoidal categories, called codifferential categories. Differential categories were introduced as the categorical framework for modelling differential linear logic. The deriving transform of a
A convenient differential
, 2010
"... In this paper, we show that the category of Mackeycomplete, separated, topological convex bornological vector spaces and bounded linear maps is a differential category. Such spaces were introduced by Frölicher and Kriegl, where they were called convenient vector spaces. While much of the structure ..."
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In this paper, we show that the category of Mackeycomplete, separated, topological convex bornological vector spaces and bounded linear maps is a differential category. Such spaces were introduced by Frölicher and Kriegl, where they were called convenient vector spaces. While much of the structure necessary to demonstrate this observation is already contained in Frölicher and Kriegl’s book, we here give a new interpretation of the category of convenient vector spaces as a model of the differential linear logic of Ehrhard and Regnier. Rather than base our proof on the abstract categorical structure presented by Frölicher and Kriegl, we prefer to focus on the bornological structure of convenient vector spaces. We believe bornological structures will ultimately yield a wide variety of models of differential logics. 1
Finiteness spaces, graphs and “coherence”
, 905
"... Abstract. We look at a subcollection of finiteness spaces introduced in [2] based on the notion of coherence spaces from [4]. The original idea was to generalize the notion of stable functions between coherence spaces to interpret the algebraic lambdacalculus ([6]) or even the differential lambda ..."
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Abstract. We look at a subcollection of finiteness spaces introduced in [2] based on the notion of coherence spaces from [4]. The original idea was to generalize the notion of stable functions between coherence spaces to interpret the algebraic lambdacalculus ([6]) or even the differential lambdacalculus ([3]). An important tool for this analysis is the infinite Ramsey theorem. 0. Introduction. The category of coherence spaces was the first denotational model for linear logic (see [4]): the basic objects are reflexive, non oriented graphs; and we are more specifically interested by their cliques (complete subgraph). If C is such a graph, we write C(C) for the collection of its cliques. Coherence spaces enjoy a very rich algebraic structure where the most important
A Completeness Theorem for “Total Boolean Functions”
, 905
"... Abstract. In [3], Christine Tasson introduces an algebraic notion of totality for a denotational model of linear logic. The notion of total boolean function is, in a way, quite intuitive. This note provides a positive answer to the question of completeness of the “boolean centroidal calculus ” w.r.t ..."
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Abstract. In [3], Christine Tasson introduces an algebraic notion of totality for a denotational model of linear logic. The notion of total boolean function is, in a way, quite intuitive. This note provides a positive answer to the question of completeness of the “boolean centroidal calculus ” w.r.t. total boolean functions.
A Completeness Theorem for “Total Boolean Functions”
"... Abstract. In [3], Christine Tasson introduces an algebraic notion of totality for a denotational model of linear logic. The notion of total boolean function is, in a way, quite intuitive. This note provides a positive answer to the question of completeness of the “boolean centroidal calculus ” w.r.t ..."
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Abstract. In [3], Christine Tasson introduces an algebraic notion of totality for a denotational model of linear logic. The notion of total boolean function is, in a way, quite intuitive. This note provides a positive answer to the question of completeness of the “boolean centroidal calculus ” w.r.t. total boolean functions.
Order algebras: a quantitative model of interaction
, 2010
"... Abstract. A quantitative model of concurrent interaction in introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential nondeterminism in synchronisation. This algebraic structure is shown to provide faithful inte ..."
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Abstract. A quantitative model of concurrent interaction in introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential nondeterminism in synchronisation. This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational (in the sense that the internal workings of processes are ignored) and noninterleaving. Constructions on algebras and their subspaces enjoy a good structure that make them (nearly) a model of differential linear logic, showing that the underlying approach to the representation of nondeterminism as linear