Environments, continuation semantics and indexed categories

1997 ◽  
pp. 391-414 ◽  
Author(s):  
John Power ◽  
Hayo Thielecke
Keyword(s):  
Indexed Categories

V-indexed categories

1978 ◽  
pp. 126-140
Author(s):  
R. J. Wood
Keyword(s):  
Indexed Categories

Indexed Categories and Their Applications

1978 ◽  
Author(s):  
Peter T. Johnstone ◽  
Robert Paré ◽  
R. D. Rosebrugh ◽  
D. Schumacher ◽  
R. J. Wood ◽  
...  
Keyword(s):  
Indexed Categories

scholarly journals Some fundamental algebraic tools for the semantics of computation: Part 3. indexed categories

1991 ◽  
Vol 91 (2) ◽  
pp. 239-264 ◽  
Author(s):  
Andrzej Tarlecki ◽  
Rod M. Burstall ◽  
Joseph A. Goguen
Keyword(s):  
Indexed Categories

scholarly journals More on Descent Theory for Schemes

2004 ◽  
Vol 11 (4) ◽  
pp. 783-800
Author(s):  
B. Mesablishvili
Keyword(s):  
Finite Type ◽  
Type Ii ◽  
Type Iv ◽  
Descent Theory ◽  
Alternative Characterization ◽  
Regular Epimorphism ◽  
Indexed Categories

Abstract In this paper we continue the investigation of some aspects of descent theory for schemes that was begun in [Mesablishvili, Appl. Categ. Structures]. Let 𝐒𝐂𝐇 be a category of schemes. We show that quasi-compact pure morphisms of schemes are effective descent morphisms with respect to 𝐒𝐂𝐇-indexed categories given by (i) quasi-coherent modules of finite type, (ii) flat quasi-coherent modules, (iii) flat quasi-coherent modules of finite type, (iv) locally projective quasicoherent modules of finite type. Moreover, we prove that a quasi-compact morphism of schemes is pure precisely when it is a stable regular epimorphism in 𝐒𝐂𝐇. Finally, we present an alternative characterization of pure morphisms of schemes.

Towards a Categorical Semantics of Type Classes

1992 ◽  
Vol 16 (2) ◽  
pp. 127-147
Author(s):  
Barney P. Hilken ◽  
David E. Rydeheard
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Functional Programming Languages ◽  
Type Classes ◽  
Indexed Categories ◽  
Categorical Semantics

This is an exercise in the description of programming languages as indexed categories. Type classes have been introduced into functional programming languages to provide a uniform framework for ‘overloading’. We establish a correspondence between type classes and comprehension schemata in categories. A coherence result allows us to describe subclasses and implicit conversions between types.

scholarly journals Models of non-well-founded sets via an indexed final coalgebra theorem

2007 ◽  
Vol 72 (3) ◽  
pp. 767-791 ◽  
Author(s):  
Benno van den Berg ◽  
Federico de Marchi
Keyword(s):  
Special Class ◽  
Indexed Categories

AbstractThe paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely complete and cocomplete categories. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide models for various non-well-founded set theories, depending on the chosen axiomatisation for the class of small maps.

Towards a uniform presentation of logical systems by indexed categories and adjoint situations

2012 ◽  
Vol 25 (1) ◽  
pp. 57-93
Author(s):  
U. Wolter ◽  
A. Martini ◽  
E. H. Hausler
Keyword(s):  
Indexed Categories

scholarly journals Coherence for bicategories and indexed categories

1985 ◽  
Vol 37 ◽  
pp. 59-80 ◽  
Author(s):  
Saunders Maclane ◽  
Robert Paré
Keyword(s):  
Indexed Categories

A category-theoretic account of program modules

1991 ◽  
Vol 1 (1) ◽  
pp. 103-139 ◽  
Author(s):  
Eugenio Moggi
Keyword(s):  
Programming Languages ◽  
Higher Order ◽  
Dependent Types ◽  
Modular Approach ◽  
Indexed Categories ◽  
Program Modules

The type-theoretic explanation of modules proposed to date (for programming languages like ML) is unsatisfactory, because it does not capture that the evaluation of type-expressions is independent from the evaluation of program expressions. We propose a new explanation based on ‘programming languages as indexed categories’ and illustrate how ML can be extended to support higher order modules, by developing a category-theoretic semantics for a calculus of modules with dependent types. The paper also outlines a methodology, which may lead to a modular approach in the study of programming languages.

Sign in / Sign up

Export Citation Format

Share Document