Results 251 to 260 of about 1,642,029 (305)

General Heart Construction on a Triangulated Category (II): Associated Homological Functor

Applied Categorical Structures, 2009
In the preceding part (I) of this paper, we showed that for any torsion pair (i.e., t-structure without the shift-closedness) in a triangulated category, there is an associated abelian category, which we call the heart.
N. Abe, H. Nakaoka
semanticscholar   +1 more source

Category-functor Modelling of Natural Systems

Cybernetics and systems, 1999
An approach to the derivation of dynamic equations for natural systems modelled by mathematical structures is suggested. The approach rests on an extremum principle which postulates that among all possible states of a system those are actually realized ...
A. Levich, A. V. Solov'Yov
semanticscholar   +1 more source

Categories and functors

1979
In this section the notion of a category is defined and some elementary examples are given. For a discussion of some aspects of the definition of a category and also for a variety of other examples, the reader can refer to: Bucur-Deleanu [1], Gabriel [1], Grothendieck—Verdier [1], Kuros-Livsic—Sulgeifer [1], Lawvere [3], Gabriel—Zisman [1], Eilenberg ...
Nicolae Popescu, Liliana Popescu
openaire   +2 more sources

Capacity functor in the category of compacta

, 2008
Spaces of upper-semicontinuous capacities on compacta are studied. It is proved that the capacity functor defines a monad in the category of compacta containing the monad of inclusion hyperspaces as a submonad.
M. Zarichnyǐ, O. Nykyforchyn
semanticscholar   +1 more source

Categories of Functors

1994
Many constructions on various mathematical objects depend not just on the elements of those objects but also on the morphisms between them. Such constructions can thus be effectively formulated in the corresponding category of objects. A “topos” is a category in which a number of the most basic such constructions (product, pullback, exponential ...
Ieke Moerdijk, Saunders Mac Lane
openaire   +2 more sources

TTF Triples in Functor Categories

Applied Categorical Structures, 2009
We characterize the hereditary torsion pairs of finite type in the functor category of a ring R that are associated to tilting torsion pairs in the category of R-modules. Moreover, we determine a condition under which they give rise to TTF triples.
ANGELERI HUEGEL L, BAZZONI, SILVANA
openaire   +4 more sources

ON THE DERIVED CATEGORY AND K-FUNCTOR OF COHERENT SHEAVES ON INTERSECTIONS OF QUADRICS

, 1989
A graded Clifford algebra connected with the complete intersection of several quadrics is considered. In terms of modules over this algebra, a description is given of the derived category of coherent sheaves and the Quillen K-functor of the intersection ...
M. Kapranov
semanticscholar   +1 more source

Categories and Functors

1974
This monograph concerns certain categories ℂ equipped with a full subcategory °ℂ with “small” or “finitely generated” objects. Both of these categories are entirely concrete. In particular the objects A, B, ℭ, ... are sets and the morphisms p, q, r, ... are maps.
J. N. Crossley, Anil Nerode
openaire   +2 more sources

Torsion Pairs in Categories of Modules over a Preadditive Category

Bulletin of the Iranian Mathematical Society, 2019
It is a result of Gabriel that hereditary torsion pairs in categories of modules are in bijection with certain filters of ideals of the base ring, called Gabriel filters or Gabriel topologies.
C. Parra, Manuel Saor'in, Simone Virili
semanticscholar   +1 more source

Behavioral Metrics via Functor Lifting

Foundations of Software Technology and Theoretical Computer Science, 2014
We study behavioral metrics in an abstract coalgebraic setting. Given a coalgebra alpha: X -> FX in Set, where the functor F specifies the branching type, we define a framework for deriving pseudometrics on X which measure the behavioral distance of ...
Paolo Baldan, F. Bonchi, Henning Kerstan, B. König   +3 more
semanticscholar   +1 more source