Essential localizations and infinitary exact completion.
Explicit cogenerators for the homotopy category of projective modules over a ring
Let be a ring. In two previous articles [12, 14] we studied the homotopy category of projective -modules. We produced a set of generators for this category, proved that the category is -compactly generated for any ring , and showed that it need not always be compactly generated, but is for sufficiently nice . We furthermore analyzed the inclusion and the orthogonal subcategory . And we even showed that the inclusion has a right adjoint; this forces some natural map to be an equivalence...
Faisceaux et complétions universelles
Families of functions dominated by distributions of -classes of mappings
A subsheaf of the sheaf of germs functions over an open subset of is called a sheaf of sub function. Comparing with the investigations of sheaves of ideals of , we study the finite presentability of certain sheaves of sub -rings. Especially we treat the sheaf defined by the distribution of Mather’s -classes of a mapping.
Fibrant presheaves of spectra and Guillén-Navarro extension
Fibrations and recursivity
Finite closed coverings of compact quantum spaces
We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...
Foncteur pleinement fidèle dense classant les algèbres
Functional separation of inductive limits and representation of presheaves by sections. Part IV: Representation of presheaves by sections
Functional separation of inductive limits and representation of presheaves by sections. Part III: Some special cases of separation of inductive limits of presheaves
Functional separation of inductive limits and representation of presheaves by sections. Part II. Embedding of presheaves into presheaves of compact spaces
Functional separation of inductive limits and representation of presheaves by sections. Part one: Separation theorems for inductive limits of closured presheaves
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX,...
GAGA for DQ-algebroids
Germs of quasi-continuous functions
Homotopy colimits in presheaf categories
Homotopy limits in triangulated categories
Infinitesimal and local structures for Banach spaces and its exponentials in a topos
Injectivity in the quasi-topo of separated presheaves on a complete Heyting algebra
Integral Domain Type Representations in Sheaves and Other Topoi.