In this paper we explore the isotropic stable motivic homotopy category constructed from usual category, following work of Vishik on motives (see [28]), by killing anisotropic varieties. particular, focus cohomology operations in realm and study structure Steenrod algebra. Then, construct an version Adams spectral sequence apply it to find a complete description groups sphere spectrum, which ha...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

We consider a multicriteria sorting procedure based on a majority rule, called MR-Sort. This procedure allows to sort each object of a set, evaluated on multiple criteria, in a category selected among a set of pre-defined and ordered categories. With MR-Sort, the ordered categories are separated by profiles which are vectors of performances on the different attributes. Using the MR-Sort rule, a...

We introduce the notion of a Hu-Liu prime ideal in the context of left commutative rngs, and establish the contravariant functor from the category of left commutative rngs into the category of topological spaces. It is well known that new points must be introduced in order to expand algebraic geometry over algebraically closed fields into Grothendieck’s scheme theory over commutative rings. We ...

we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.

The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category modadm(E) of admissibly finitely presented functors and use it to give version for any exact E. An important ingredient proof localization theory categories. We also investigate how properties E are reflected modadm(E), example being (weakly) idempotent complete or having eno...