Equilogical spaces, homology and non-commutative geometry
Erratum to “Convenient vector spaces embed into the Cahiers topos”
Espaces d'Antoine et pseudo-topologies
Exploring the gap between linear and classical logic.
Exponentiability in categories of lax algebras. (Dedicated to Nico Pumplün on the occasion of his seventieth birthday).
Exponentiability of perfect maps: Four approaches.
Exponentiable morphisms: Posets, spaces, locales, and Grothendieck toposes.
Exponential objects in the construct
Exponentiality in categories of partial algebras.
Extending tensor products to structures of closed categories
Fermeture standard des catégories algébriques II
Functorial polymorphism and semantic parametricity
Galois H-objects with a normal basis in closed categories. A cohomological interpretation.
In this paper, for a cocommutative Hopf algebra H in a symmetric closed category C with basic object K, we get an isomorphism between the group of isomorphism classes of Galois H-objects with a normal basis and the second cohomology group H2(H,K) of H with coefficients in K. Using this result, we obtain a direct sum decomposition for the Brauer group of H-module Azumaya monoids with inner action:BMinn(C,H) ≅ B(C) ⊕ H2(H,K)In particular, if C is the symmetric closed category of C-modules with K a...
Gaps and dualities in Heyting categories
We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.
Graphs of morphisms of graphs.
Inner actions and Galois -objects in a symmetric closed category
Internal object actions
We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module.
Internal presheaves toposes
Isomorphisms between left and right adjoints.
Lax-co-limites structurées