Definability and approximations in triangulated categories
Rosanna Laking, Jorge Vitória
Abstract
We give criteria for subcategories of a compactly generated algebraic triangulated category to be precovering or preenveloping. These criteria are formulated in terms of closure conditions involving products, coproducts, directed homotopy colimits and further conditions involving the notion of purity. In particular, we provide sufficient closure conditions for a sub-category of a compactly generated algebraic triangulated category to be a torsion class. Finally we explore applications of the previous results to the theory of recollements.
Topics & Concepts
MathematicsSubcategoryCoproductTriangulated categoryHomotopy categoryTorsion (gastropod)Pure mathematicsClosure (psychology)Algebraic numberClass (philosophy)HomotopyAlgebra over a fieldDerived categoryMathematical analysisFunctorComputer scienceArtificial intelligenceMedicineSurgeryEconomicsMarket economyAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in Algebra