Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].

In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective s...

Abstract Palu defined the index with respect to a cluster tilting object in suitable triangulated category, order better understand Caldero–Chapoton map that exhibits connection between algebras and representation theory. We push this further by proposing an contravariantly finite, rigid subcategory, we show behaves similarly classical index. Let ${\mathcal{C}}$ be skeletally small category spl...

Let Fp denote the field with p elements and F̄p its algebraic closure. We show that the singular cochain functor with coefficients in F̄p induces a contravariant equivalence between the homotopy category of connected pcomplete nilpotent spaces of finite p-type and a full subcategory of the homotopy category of E∞ F̄p-algebras. Draft: January 26, 1998, 17:28

We show that every λm-injectivity class (i.e., the class of all the objects injective with respect to some class of λ-presentable morphisms) is a weakly reflective subcategory determined by a functorial weak factorization system cofibrantly generated by a class of λ-presentable morphisms. This was known for small-injectivity classes, and referred to as the “small object argument”. An analogous ...

We prove the universal property of the infinitary exact completion of a category with weak small limits. As an application, we slightly weaken the conditions characterizing essential localizations of varieties (in particular, of module categories) and of presheaf categories. Introduction An essential localization is a reflective subcategory such that the reflector has a left adjoint. In [12], R...

We exhibit a triangulated category T having both products and coproducts and a triangulated subcategory S ⊂ T which is both localizing and colocalizing, and for which neither a Bousfield localization nor a colocalization exists. It follows that neither the category S nor its dual satisfy Brown representability. Our example involves an abelian category whose derived category does not have small ...

This essay is an attempt to reconsider what vision of-that is, what discourse on-Buddhist icons is possible for a Westerner (or Westernized Asian). Buddhist icons have been essentially the domain, or rather the preserve, of art historians. But Buddhist art, if there is such a thing, is perhaps too important to be left to art historians alone. Is there a Buddhist "art," a subcategory of Asian ar...

In this paper we unfold the 2-category structure of the representations of a (strict) 2-group on (a suitable version of) Kapranov and Voevodsky’s 2-category of finite dimensional 2-vector spaces and we discuss the relationship with classical representation theory of groups on finite dimensional vector spaces. In particular, we prove that the monoidal category of representations of any group G a...

We prove that AW*-algebras are determined by their projections, their symmetries, and the action of the latter on the former. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-al...