Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics.
Rewriting on cyclic structures : equivalence between the operational and the categorical description
Rewriting on cyclic structures: Equivalence between the operational and the categorical description
We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2-theories. We show that this presentation is equivalent to the well-accepted operational definition proposed by Barendregt et al. – but for the case of circular redexes , for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and...
Sémantique catégorique des constructeurs de types d'ordre supérieur
Semigroups with S.M.F. structures.
Solving algebraic equations using coalgebra
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable...
Solving Algebraic Equations Using Coalgebra
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable ...
Stable surjection logic
Strong functors and interleaving fixpoints in game semantics
We describe a sequent calculus μLJ with primitives for inductive and coinductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ. We then turn to the construction of a concrete μ-closed category based on Hyland-Ong game semantics. The model relies on three main ingredients:...
Structures algébriques : thème et variations
Structures defined by finite limits in the enriched context, I
Structures pseudo-algébriques (1ère partie)
Sur la caractérisation sémantique des catégories de structures
Sur les produits tensoriels extérieurs de structures algébriques
Sur quelques problèmes de plongement en algèbre
Sur quelques problèmes de plongements en algèbre
Sur quelques structures de base pour définir les structures
Syntactical theory of functors
is a quasi-variety
The algebraic theory of moving frames