Let G be a finite group. We use the results of [5] to show that the Tate homology of E(n) local spectra with respect to G produces E(n− 1) local spectra. We also show that the Bousfield class of the Tate homology of LnX (for X finite) is the same as that of Ln−1X. To be precise, recall that Tate homology is a functor from G-spectra to G-spectra. To produce a functor PG from spectra to spectra, ...

In this paper, we study the completion of fuzzy quasi-uniform spaces from a categorical point view. Firstly, introduce concept prorelations and describe as enriched categories. Then construct Yoneda embedding in through promodules, prove validness Lemma for right adjoint promodules. Finally, Cauchy by embedding. We show that inclusion functor category T0 separated complete to quasiuniform has l...

A covariant functor from category of complex tori to the category of noncommutative tori is constructed. The functor maps isomorphic complex tori to the Morita equivalent noncommutative tori. Our construction is based on the Teichmüller theory of Riemann surfaces.

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...

After defining, for each many-sorted signature Σ = (S,Σ), the category Ter(Σ), of generalized terms for Σ (which is the dual of the Kleisli category for TΣ, the monad in Set determined by the adjunctionTΣ ⊣ GΣ from Set toAlg(Σ), the category of Σ-algebras), we assign, to a signature morphism d from Σ to Λ, the functor d⋄ from Ter(Σ) to Ter(Λ). Once defined the mappings that assign, respectively...

The notion of open-multicommutativity, introduced by Kozhan and Zarichnyi [5], is investigated. The weakly normal covariant functor of upper-continuous capacities is considered. The main result of the paper is that this functor open-multicommutative.

A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on the rank of an elliptic curve is formulated.

Cuntz and Quillen have shown that for algebras over a field k with char(k) = 0, periodic cyclic homology may be regarded, in some sense, as the derived functor of (non-commutative) de Rham (co-)homology. The purpose of this paper is to formalize this derived functor analogy. We show that the localization DefPA of the category PA of countable pro-algebras at the class of (infinitesimal) deformat...

It is well-known that the construction of space of probability measures P is functorial in the category Comp of compact Hausdorff spaces. The functor P is normal in the sense of E.V. Shchepin [1]. It is well-known that the functor P is open, i.e. it preserves the class of open surjective maps. This was first proved by Ditor and Eifler [2]. E.V. Shchepin [1] discovered tight relations between th...