A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of...

A category with finite products and finite coproducts is said to be distributive if the canonical map A×B + A×C → A× (B + C) is invertible for all objects A, B, and C. Given a distributive category D , we describe a universal functor D → Dex preserving finite products and finite coproducts, for which Dex is extensive; that is, for all objects A and B the functor Dex/A × Dex/B → Dex/(A + B) is a...

Let G = SpecA be an affine functor of monoids. We prove that A∗ is the enveloping functor of algebras of G and that the category of Gmodules is equivalent to the category of A∗-modules. Moreover, we prove that the category of affine functors of monoids is anti-equivalent to the category of functors of affine bialgebras. Applications of these results include Cartier duality, neutral Tannakian du...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular...

Given an exact Lagrangian embedding Q ⊂ M , we construct an A∞ restriction functor from the wrapped Fukaya category of M to the category of modules on the differential graded algebra of chains over the based loop space of Q. If M is the cotangent bundle of Q, this functor induces an A∞ equivalence between the wrapped Floer cohomology of a cotangent fibre and the chains over the based loop space...

We show that the category A(G) of actions of a locally compact group G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of norm...

We consider the semigroup Ext(A, B) of extensions of a separable C *-algebra A by a stable C *-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext −1/2 (A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext 1/2 (A, B) is homotopy invariant and that it coincides with the functor of homoto...

Kurz et al. have recently shown that infinite λ-trees with finitely many free variables modulo α-equivalence form a final coalgebra for a functor on the category of nominal sets. Here we investigate the rational fixpoint of that functor. We prove that it is formed by all rational λtrees, i.e. those λ-trees which have only finitely many subtrees (up to isomorphism). This yields a corecursion pri...

Given a functor T : C → D carrying a class of morphisms S ⊂ C into a class S ⊂ D, we give sufficient conditions in order that T induces an equivalence on the localised categories. These conditions are in the spirit of Quillen’s theorem A. We give some applications in algebaic and birational geometry. Introduction Let T : C → D be a functor and S ⊂ C, S ⊂ D two classes of morphisms containing id...

We introduce the notion of infinitary interpretation of structures. In general, an interpretation between structures induces a continuous homomorphism between their automorphism groups, and furthermore, it induces a functor between the categories of copies of each structure. We show that for the case of infinitary interpretation the reversals are also true: Every Baire-measurable homomorphism b...