Let R and S be arbitrary associative rings. Given a bimodule RWS , we denote by ∆? and Γ? the functors Hom?(−, W ) and Ext?(−, W ), where ? = R or S. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W , finitely generated or homomorphic image of a finite direct sum of copies of W , ΓM = 0 = Ext(M, W ). We are able to describe, on a larg...

With Fq a finite field of characteristic p, let F(q) be the category whose objects are functors from finite dimensional Fq–vector spaces to F̄p– vector spaces. Extension groups in F(q) can be interpreted as MacLane (or Topological Hochschild) cohomology with twisted coefficients. Furthermore, evaluation on an m dimensional vector space Vm induces a homorphism from Ext F(q) (F, G) to finite group...

The article is devoted to extension groups in the category of functors from a small category to an additive category with an Abelian structure in the sense of Heller. It is proved that under additional assumptions there exists a spectral sequence which converges to the extension groups.

Let R be a commutative ring with unit and F denotes the category of functors from the category of R-modules to itself. Let I ∈ F denote the inclusion functor. For a functor F ∈ F we compare the groups ExtF (I, F ) with ⊕iExtF (I, LiF ) and the hyperext groups Ext∗(I,QF ), where LiF is the ith left stable derived functor of F and QF denotes the Mac Lane’s Q-construction related to F . The dual s...

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then characterize it in terms of the U -resolution dimension of some special injective modules and the property of the functors Ext(Ext(−, U), U) preserving monomorphisms, which develops a classical result of Auslander....

We analyze the geometry of the Ext-quiver of a coalgebra C in order to study the behavior of simple and injective C-comodules under the action of the functors associated to a localizing subcategory of the category of C-comodules.

Unstable modules over the Steenrod algebra with only top $k$ operations are introduced in language of ringoids. We prove category such has homological dimension at most $k$. A pratical method, which generalizes $\Lambda$ complex, to compute $\mathrm{Ext}$ group from spheres is proposed. also able establish several functors relate and unstable algebra, describe connections between groups them.

Mackey functors are a framework having the common properties of many natural constructions for finite groups, such as group cohomology, representation rings, the Bumside ring, the topological K-theory of classifying spaces, the algebraic K-theory of group rings, the Witt rings of Galois extensions, etc. In this work we first show that the Mackey functors for a group may be identified with the m...

Abstract Pirashvili’s Dold–Kan type theorem for finite pointed sets follows from the identification in terms of surjections morphisms between tensor powers a functor playing role augmentation ideal; these functors are projective. We give an unpointed analogue this result: namely, we compute corresponding context. also calculate Ext groups such objects, particular showing that not projective; is...