Congruences In Regular Categories.
Epireflections which are completions
Exact completion and representations in abelian categories.
Extensions of factorization systems
Extremal subobjects of complete posets
Factorization, fibration and torsion.
Factorization systems and adjunctions.
Factorization systems for symmetric cat-groups.
Factorization theorems for geometric morphisms, I
Free Quillen factorization systems.
Further criteria for totality
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.
Homomorphism theorem for equationally partial algebras
Images in categories as reflections
Injectivity versus exponentiability
Internal monotone-light factorization for categories via preorders.
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.
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.
Note on universal topological completion