Rational fibrations in differential homological algebra.
Realcompactification of frames
We give a construction of Wallman-type realcompactifications of a frame by considering regular sub -frames the join of which generates . In particular, we show that the largest such regular sub -frame gives rise to the universal realcompactification of .
Realization of Cartesian Closed Topological Hulls.
Realization of long exact sequences of abelian groups.
Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories...
Realization of small concrete categories by algebras and injective homomorphisms
Realizations of topologies and closure operators by set systems and by neighbourhoods
Recollement of colimit categories and its applications
We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and -groups.
Recursive coalgebras of finitary functors
For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.
Récursivité graphique (1e partie) : catégorie des fonctions récursives primitives formelles
Reducing inverse systems of monomorphisms
Reedy categories which encode the notion of category actions
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
Refining thick subcategory theorems
We use a K-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some commutative rings. In the stable homotopy category of spectra we obtain only...
Reflections in locally presentable categories
Reflections on distal spaces
Reflective and coreflective subcategories of Unif (and Top)
Reflective functors via nearness
Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads.
Reflective Mac Neille completions of fibre-small categories need not be fibre-small
Reflective subcategories and dense subcategories
Reflective subcategories of Poset and Top