Décompositions et Lax-complétions
Deduction over graphs under constraints : a soundness and completeness theorem
Definable orthogonality classes in accessible categories are small
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka’s principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy. For example, the statement that, for a class of morphisms in a locally presentable category of structures, the orthogonal class of objects is a small-orthogonality...
Demonic semantics: using monotypes and residuals.
Dense morphisms of monads.
Descent for monads.
Descent in categories of (co)algebras.
Dialectica and Chu constructions: cousins?
Differential algebra in a topos
Distributive adjoint strings.
Distributive laws and Koszulness
Distributive law is a way to compose two algebraic structures, say and , into a more complex algebraic structure . The aim of this paper is to understand distributive laws in terms of operads. The central result says that if the operads corresponding respectively to and are Koszul, then the operad corresponding to is Koszul as well. An application to the cohomology of configuration spaces is given.
Distributive laws. Applications to stochastic automata. (Lois distributives. Applications aux automates stochastiques.)
Distributive laws for pseudomonads.
Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras
We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.
Doctrines on 2-Categories.
Doctrines whose structure forms a fully faithful adjoint string.
D'où viennent les esquives ?
Dualities of concrete categories
Duality for some free modes
The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.