This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

Let Γg,n, for 2g − 2 + n > 0, be the Teichmüller group of an n-punctured genus g compact Riemann surface Sg,n and let Γ̂g,n be its profinite completion. There is a natural homomorphism from the Galois cohomology of Γ̂g,n, with coefficients in a discrete torsion Γ̂g,n-module, to the cohomology of the discrete group Γg,n, with induced coefficients. The main result of this paper is that this map is a...

Let G be a finite group, and R be a commutative ring. This note proposes a generalization to any Green functor for G over R of the construction of the Hochschild cohomology ring HH∗(G,R) from the ordinary cohomology functor H∗(−, R). Another special case is the construction of the crossed Burnside ring of G from the ordinary Burnside functor. The general abstract setting is the following : let ...

Jacobians of degenerating families curves are well-understood over 1-dimensional bases due to work Néron and Raynaud; the fundamental tool is model its description via Picard functor. Over higher-dimensional models typically do not exist, but in this paper we construct a universal base change ? ˜ g,n ?? ¯ after which N /? jacobian does exist. This yields new partial compactification moduli spac...

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.

Let k be a field of characteristic p. We construct a new inflation functor for cohomological Mackey functors for finite groups over k. Using this inflation functor, we give an explicit presentation of the graded algebra of self extensions of the simple functor S 1 , when p is odd and G is an elementary abelian p-group. AMS Subject Classification : 18A25, 18G10, 18G15, 20J05.

We study the functor `2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and both categories are enriched over algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its ...