For a Hopf algebra H over a commutative ring k, the category MH of right Hopf modules is equivalent to the category Mk of k-modules, that is, the comparison functor −⊗k H : Mk → MH is an equivalence (Fundamental theorem of Hopf modules). This was proved by Larson and Sweedler via the notion of coinvariants McoH for any M ∈ MH . The coinvariants functor (−) coH : MH → Mk is right adjoint to the ...

It is well-known that every homology functor on the stable homotopy category is representable, so of the form E∗(X) = π∗(E ∧ X) for some spectrum E. However, Christensen, Keller, and Neeman [CKN01] have exhibited simple triangulated categories, such as the derived category of k[x, y] for sufficiently large fields k, for which not every homology functor is representable. In this paper, we show t...

Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...

" First quantization is a mystery, but second quantization is a func-tor " (E. Nelson) Comme l'on sait la " quantification geometrique " consiste a rechercher un certain foncteur de la categorie des varietes symplectiques et sym-plectomorphismes dans celle des espaces de Hilbert complexes et des transformations unitaires (.. .) Il est bien connu qu'un tel foncteur n'existe pas. Abstract We defi...

We describe a symplectization functor from the Poisson category to the symplectic “category” and we study some of its properties.

We introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces. More exactly, for each continuous t-norm we prove that the category of all fuzzy uniform spaces in our sense (and fuzzy uniformly continuous mappings) is isomorphic to the category of uniform spaces (and uniformly continuous mappings) by means of a covariant func...

We explain (following V. Drinfeld) how the G(C[[t]]) equivariant derived category of the affine Grassmannian can be described in terms of coherent sheaves on the Langlands dual Lie algebra equivariant with respect to the adjoint action, due to some old results of V. Ginzburg. The global cohomology functor corresponds under this identification to restriction to the Kostant slice. We extend this ...

General methods of investigating e ectivity on regular Hausdor (T3) spaces is considered. It is shown that there exists a functor from a category of T3 spaces into a category of domain representations. Using this functor one may look at the subcategory of e ective domain representations to get an e ectivity theory for T3 spaces. However, this approach seems to be beset by some problems. Instead...

In (non-commutative) geometry, a categorical resolution of a (potentially singular) variety X is a full and faithful embedding of its derived category D(X) into a smooth and proper triangulated category T [11, 12]. The notion generalises the situation of rational singularities, where the geometric resolution functor F : X̃ → X induces the full and faithful functor F ∗ : D(X) → D(X̃) to the smooth...

We introduce and develop the notion of scalar extension for abelian categories. Given a field extension F /F , to every F -linear abelian category A satisfying a suitable finiteness condition we associate an F -linear abelian category A ⊗F F ′ and an exact F -linear functor t : A → A ⊗F F . This functor is universal among F -linear right exact functors with target an F -linear abelian category....