منابع مشابه
The Maximality of Cartesian Categories
It is proved that equations between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equation in the language of free cartesian categories collapses a cartesian category into a preorder. An analogous result holds for categories with binary products, which may lack a terminal object. The proof is based on a coherence result for cartesian categorie...
متن کاملThe Maximality of Cartesian Categories
It is proved that equations between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equation in the language of free cartesian categories collapses a cartesian category into a preorder. An analogous result holds for categories with binary products, which may lack a terminal object. The proof is based on a coherence result for cartesian categorie...
متن کاملThe Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories
From the analogue of Böhm’s Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here of these results, which were obtained previously by Richard Statman and Alex K. Simpson. Mathema...
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...
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...
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ژورنال
عنوان ژورنال: MLQ
سال: 2001
ISSN: 0942-5616,1521-3870
DOI: 10.1002/1521-3870(200101)47:1<137::aid-malq137>3.0.co;2-f