Natural factorizations and the Kan extension of cohomology theories
Natural sinks on
Let be the large source of epimorphisms in the category of Urysohn spaces constructed in [2]. A sink is called natural, if for all . In this paper natural sinks are characterized. As a result it is shown that permits no -factorization structure for arbitrary (large) sources.
Natural weak factorization systems
In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category is introduced, as a pair (comonad, monad) over . The link with existing notions in terms of morphism classes is given via the respective Eilenberg–Moore categories.
Near reflections
Non-constant continuous maps of modifications of topological spaces
Normalgruppoide einer Kategorie
Normalisation of the theory of Cartesian closed categories and conservativity of extensions of
Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T[x] of T
Using an inductive definition of normal terms of the theory of Cartesian Closed Categories with a given graph of distinguished morphisms, we give a reduction free proof of the decidability of this theory. This inductive definition enables us to show via functional completeness that extensions of such a theory by new constants (“indeterminates”) are conservative.
Note about atom-categories of topological spaces
Note on Demi-Topological Functors.
Note on dense covers in the category of locales
In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.
Note on homomorphism interpolation theorem
Note on homotopy pullbacks in abelian categories
Note on universal topological completion
Notes on enriched categories with colimits of some class.
Notions of flatness relative to a Grothendieck topology.