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𝒯 0 - and 𝒯 1 -reflections

Maria Manuel Clementino (1992)

Commentationes Mathematicae Universitatis Carolinae

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms T 0 and T 1 . Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.

A categorical concept of completion of objects

Guillaume C. L. Brümmer, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.

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