We prove a conjecture of Rognes that establishes a localization cofiber sequence of spectra K(Z) → K(ku) → K(KU) → ΣK(Z) for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage theorem identifying the K-theory of the Waldhausen category of Postnikov towers of modules over a connective A∞ ring spectrum R with the Quillen K-theo...

elementary classes (Shelah 1987) form a special case of the former (Lieberman 2011, Beke and JR 2012) and generalize Lκω-elementary classes. Surprisingly, I do not know any abstract elementary class which does not have an Lκω-axiomatization (as an abstract category). With Makkai, we failed to prove that uncountable sets with injective mappings form such an example. It seemed a long time that th...

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street’s weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories Wdl(K), of (n + 1)-tuples of monads in K pairwise related by weak distributive laws obeying the Yang-Baxter equation. The first instance Wdl(K) coincides with Mnd(K),...

The purpose of this paper is to studying nonlinear k-ε turbulence models and its advantages in internal combustion engines, since the standard k-ε model is incapable of representing the anisotropy of turbulence intensities and fails to express the Reynolds stresses adequately in rotating flows. Therefore, this model is not only incapable of expressing the anisotropy of turbulence in an engine c...

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group [18, 9].

This research was motivated by universal algebraic geometry. One of the central questions of universal algebraic geometry is: when two algebras have the same algebraic geometry? For answer of this question (see [8],[10]) we must consider the variety Θ, to which our algebras belongs, the category Θ of all finitely generated free algebras of Θ and research how the group AutΘ of all the automorphi...

Let k be a field and A a finite dimensional (associative with 1) k-algebra. By modA we denote the category of finite dimensional left A-modules. In many important situations we may suppose that A is presented as a quiver with relations (Q, I) (e.g. if k is algebraically closed, then A is Morita equivalent to kQ/I). We recall that if A is presented by (Q, I), then Q is a finite quiver and I is a...

The additivity theorem for comlicial dérivateurs is proved. Also, to any exact category in the sense of Quillen a K-theory space is associated. This K-theory is shown to satisfy the additivity, approximation and resolution theorems. CONTENTS 1. Introduzione 1 2. Chain complexes, homotopies, derived categories 3 2.1. Definition of the derived category 3 2.2. Homotopy pullbacks and homotopy pusho...

Every endofunctor F of Set has an initial algebra and a final coalgebra, but they are classes in general. Consequently, the endofunctor F∞ of the category of classes that F induces generates a completely iterative monad T . And solutions of arbitrary guarded systems of iterative equations w.r.t. F exist, and can be found in naturally defined subsets of the classes TY . More generally, starting ...