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Universal monos in partial morphism categories. (English) Zbl 1192.18001

In this paper the authors consider the partial morphism category \( \overrightarrow{\mathcal C}\) associated to an arbitrary category \(\mathcal C.\) The partial morphisms may be limited as to the type of subobject on which they are defined. Such limitations are determined by a further domain structure on the category \(\mathcal C\). The main thrust of the paper is to classify and describe those monos in \(\overrightarrow{\mathcal C}\) which admit arbitrary pullbacks. The results depend on the logical structure of the posets of subobjects of objects in \(\mathcal C\).

MSC:

18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18A15 Foundations, relations to logic and deductive systems
18B15 Embedding theorems, universal categories
18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
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