The aim of the first part is to explain, how some geometric questions can be translated to the language of representation theory. There will be three categories of representations of G: Sm G ⊃ I G ⊃ Adm, roughly corresponding to birational geometry, to birational motivic questions (like structure of Chow groups of 0-cycles) and to " finite-dimensional " birational motivic questions (in particul...

We study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2categories. Using these results, we describe the homotopical behaviour not only of conical limits but also of weighted limits. Finally, pseudo-limits are related to homotopy limits. 1. Quillen model structu...

Introduction Exposure to chronic levels of ionizing radiation could be detrimental to health even at very low doses. Calabar free trade zone (CFTZ) was established to promote export business in Nigeria and it is yet to produce exposure data of the Zone. Materials and Methods The Zone was divided into three categories depending on the type of business. Category A had facilities with manufacturin...

This paper presents a work whose aim is to obtain information on execution time of λ-terms by semantic means. By execution time, we mean the number of steps in a computational model. As in [Ehrhard and Regnier 2006], the computational model considered in this paper will be Krivine’s machine, a more realistic model than β-reduction. Indeed, Krivine’s machine implements (weak) head linear reducti...

This paper presents a work whose aim is to obtain information on execution time of λ-terms by semantic means. By execution time, we mean the number of steps in a computational model. As in [Ehrhard and Regnier 2006], the computational model considered in this paper will be Krivine’s machine, a more realistic model than β-reduction. Indeed, Krivine’s machine implements (weak) head linear reducti...

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C| = BC. We study the ring homomorphism HH∗(kC) → H∗(|C|, k) and prove it is split surjective, using the factorization category of Quillen [16] and certain techniques from functor cohomology theory. This generalizes the well-known results for finite groups...

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

We introduce categories of homogeneous strict polynomial functors, Pold,k and Pol II d,k, defined on vector superspaces over a field k of characteristic not equal 2. These categories are related to polynomial representations of the supergroups GL(m|n) and Q(n). In particular, we prove an equivalence between Pold,k, Pol II d,k and the category of finite dimensional supermodules over the Schur su...

Let k be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian p-adic Lie extensions E/F , where F is a local field with residue field k, and a category whose objects are pairs (K,A), where K ∼= k((T )) and A is an abelian p-adic Lie subgroup of Autk(K). In this paper we extend this equivalence to allow Gal(E/F ...