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Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
A Theory of Recursive Domains with Applications to Concurrency
 In Proc. of LICS ’98
, 1997
"... Marcelo Fiore , Glynn Winskel (1) BRICS , University of Aarhus, Denmark (2) LFCS, University of Edinburgh, Scotland December 1997 Abstract We develop a 2categorical theory for recursively defined domains. ..."
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Cited by 23 (14 self)
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Marcelo Fiore , Glynn Winskel (1) BRICS , University of Aarhus, Denmark (2) LFCS, University of Edinburgh, Scotland December 1997 Abstract We develop a 2categorical theory for recursively defined domains.
Aspects of predicative algebraic set theory I: Exact Completion
 Ann. Pure Appl. Logic
"... This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on ..."
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Cited by 10 (2 self)
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This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on
Aspects of predicative algebraic set theory II: Realizability. Accepted for publication in Theoretical Computer Science
 In Logic Colloquim 2006, Lecture Notes in Logic
, 2009
"... This is the third in a series of papers on algebraic set theory, the aim of which is to develop a categorical semantics for constructive set theories, including predicative ones, based on the notion of a “predicative category with small maps”. 1 In the first paper in this series [8] we discussed how ..."
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Cited by 7 (1 self)
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This is the third in a series of papers on algebraic set theory, the aim of which is to develop a categorical semantics for constructive set theories, including predicative ones, based on the notion of a “predicative category with small maps”. 1 In the first paper in this series [8] we discussed how these predicative categories
Sheaves for predicative toposes
 ArXiv:math.LO/0507480v1
"... Abstract: In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal systems. Among our technical results, we prove that ..."
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Cited by 3 (0 self)
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Abstract: In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal systems. Among our technical results, we prove that all the notions of a “predicative topos ” that we consider, are stable under presheaves, while most are stable under sheaves. 1
Algebraic Set Theory and the Effective Topos
, 2004
"... Abstract Following the book Algebraic Set Theory from Andr'e Joyal and Ieke Moerdijk [8], we give a characterization of the initial ZFalgebra, for Heyting pretoposes equipped with a class of small maps. Then, an application is considered (the effective topos) to show how to recover an already known ..."
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Cited by 1 (0 self)
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Abstract Following the book Algebraic Set Theory from Andr'e Joyal and Ieke Moerdijk [8], we give a characterization of the initial ZFalgebra, for Heyting pretoposes equipped with a class of small maps. Then, an application is considered (the effective topos) to show how to recover an already known model (McCarty [9]). Introduction When looking at models for unrestricted intuitionistic set theory IZF, one is naturally led to consider categorical models, since the internal logic governing categories is, in general, intuitionistic. In their book [8], Andr'e Joyal and Ieke Moerdijk proposed a new approach to set theory which is particularly suitable for categorical treatment, being essentially algebraic and entirely constructive.
Wellfoundedness in Realizability
, 2005
"... Introduction Let < be a binary relation on a set X. In ZFC, the following three statementsare equivalent: 1) There are no infinite <descending sequences in X: i.e. no sequences( ..."
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Cited by 1 (0 self)
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Introduction Let < be a binary relation on a set X. In ZFC, the following three statementsare equivalent: 1) There are no infinite <descending sequences in X: i.e. no sequences(
SET THEORY FOR CATEGORY THEORY
, 810
"... Abstract. Questions of settheoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical co ..."
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Abstract. Questions of settheoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical constructions are permissible. In this expository paper we summarize and compare a number