Recursive coalgebras of finitary functors
For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.
Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads.
Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics.
Relative injectivity as cocompleteness for a class of distributors.
Remarks on topologically algebraic functors
Remarques sur les machines et les structures
Representable T-categories. (T-catégories représentables.)
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...