A unifying view of all constructions of pushouts of partial morphisms
considered so far in the literature of single-pushout transformation
is given in this paper. Pushouts of partial morphisms are studied in
an abstract category of spans formed out of two distinguished
subcategories of the base category, thus generalizing previous studies
in single-pushout transformation. Such spans are single pairs of
morphisms, instead of equivalence classes, providing then a notion of
transformation which is independent of class representatives.
A necessary and sufficient condition for the existence of the pushout
of two spans is established which involves properties of the base
category, from which the category of spans is derived, as well as
properties of the spans themselves. Moreover, a necessary and
sufficient condition for single-pushout derivations in a category of
spans to subsume double-pushout derivations in the base category is
established which only involves properties of the base category.
CitationMontserrat, M., Francesc, R., Torrens, J., Valiente, G. "Single-pushout rewriting in categories of spans I: the general setting". 1997.
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