Functional completeness of cartesian categories
نویسندگان
چکیده
منابع مشابه
Cartesian 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...
متن کاملDependent Cartesian Closed Categories
We present a generalization of cartesian closed categories (CCCs) for dependent types, called dependent cartesian closed categories (DCCCs), which also provides a reformulation of categories with families (CwFs), an abstract semantics for Martin-Löf type theory (MLTT) which is very close to the syntax. Thus, DCCCs accomplish mathematical elegance as well as a direct interpretation of the syntax...
متن کاملCartesian effect categories are Freyd-categories
Most often, in a categorical semantics for a programming language, the substitution of terms is expressed by composition and finite products. However this does not deal with the order of evaluation of arguments, which may have major consequences when there are side-effects. In this paper Cartesian effect categories are introduced for solving this issue, and they are compared with strong monads,...
متن کاملCartesian closed Dialectica categories
When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability interpretation and Kreisel’s modified realizability) Gödel’s Dialectica interpretation gives rise to ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1974
ISSN: 0003-4843
DOI: 10.1016/0003-4843(74)90003-5