Let G = SpecA be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗ = R × B∗ as R-algebras and the first projection A∗ → R is the unit of A. If M is a dual functor of G-modules and wG := (1, 0) ∈ R×B ∗ =...

BCK-modules were introduced as an action of a BCK-algebra over Abelian group. Homomorphisms form exact sequence which is called BCK-sequence. In this paper, we study homomorphisms BCK-modules. We show that have module structure. Moreover, sequences Hom functors are BCK-sequences.

In the present paper a logically exact way is presented in order to define approximative functors on object level in the partial first–order logic relying on approximation spaces. By the help of defined approximative functors one can determine what kind of approximations has to be taken into consideration in the evaluating process of a formula. The representations of concepts (properties) of ou...

We introduce and develop the notion of scalar extension for abelian categories. Given a field extension F /F , to every F -linear abelian category A satisfying a suitable finiteness condition we associate an F -linear abelian category A ⊗F F ′ and an exact F -linear functor t : A → A ⊗F F . This functor is universal among F -linear right exact functors with target an F -linear abelian category....

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of these functors. In particular, we show that they map irreducible spherical representations to irreducible spherical representations and, moreover, that they...

The very nature of the so-called Postnikov invariants is carefully studied. Two functors, precisely defined, explain the exact nature of the connection between the category of topological spaces and the category of Postnikov towers. On one hand, these functors are in particular effective and lead to concrete machine computations through the general machine program Kenzo. On the other hand, the ...

We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category. Moreover, the functors belonging to the stable derivator can be turned into exact functors with respect to these triangulated structures. Along the way, we give a ...

In previous work, we develop a generalized Waldhausen $S_{\bullet}$-construction whose input is an augmented stable double Segal space and output unital 2-Segal space. Here, prove that this construction recovers the previously known $S_{\bullet}$-constructions for exact categories $(\infty,1)$-categories, as well relative functors.

Rickard proved that for certain self-injective algebras, a stable equivalence induced from an exact functor is of Morita type, in the sense Broué. In this paper we study singular equivalences finite-dimensional algebras tensor product functors. We prove Gorenstein tensoring with suitable complex bimodules induces type level, Wang. This recovers Rickard's theorem case.

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.