Finitely presentable morphisms in exact sequences.
Frame monomorphisms and a feature of the -group of Baire functions on a topological space
“The kernel functor” from the category of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In , monics are one-to-one, but not necessarily so in LFrm. An embedding for which is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The -objects every embedding of which is KI are characterized;...
Functionally Hausdorff spaces
-monomorphisms
Generalized congruences – epimorphisms in .
Hereditarity of closure operators and injectivity
A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let be a regular closure operator induced by a subcategory . It is shown that, if every object of is a subobject of an -object which is injective with respect to a given class of monomorphisms, then the closure operator is hereditary with respect to that class of monomorphisms.
HSP subcategories of Eilenberg-Moore algebras.
Images in categories as reflections
Initial Morphisms and Monomorphisms.
Injectivity versus exponentiability
Isomorphisms and splitting of idempotents in semicategories
Kappa-Slender Modules
For an arbitrary infinite cardinal , we define classes of -cslender and -tslender modules as well as related classes of -hmodules and initiate a study of these classes.
Large systems of independent objects in concrete categories. I
Large systems of independent objects in concrete categories. II
Limits and colimits in certain categories of spaces of continuous functions [Book]
Linking the closure and orthogonality properties of perfect morphisms in a category
We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.
Local extension of maps.
Making factorizations compositive
The main aim of this paper is to obtain compositive cone factorizations from non-compositive ones by itereration. This is possible if and only if certain colimits of (possibly large) chains exist. In particular, we show that (strong-epi, mono) factorizations of cones exist if and only if joint coequalizers and colimits of chains of regular epimorphisms exist.
Monomorphisms and epimorphisms in abstract categories
Monomorphisms and epimorphisms of inverse systems