Research Article

Lax pullback complements in partial morphism categories

Published in: Quaestiones Mathematicae
Volume 47 , issue 4 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 777–795
DOI: 10.2989/16073606.2023.2256976
Author(s): S.N. Hosseini Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Iran, L. Yeganeh Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Iran,
Keywords: 18A30, 18B10, 18B25, 18B50, (Distributivity) pullback, (lax) pullback complement, (couniversal, exponentiable, admissible) morphism, (adhesive, cohesive, extensive, partial morphism, polynomial) category, graph rewriting,
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Abstract

The goal of this article is to characterize the lax pullback complement of a given partial morphism along a total morphism, in an -partial morphism category, where is an exponentiable stable system. To achieve this, we first show that if a lax pullback complement of a partial morphism exists in the partial morphism category, then a lax pullback complement of its total part exists in the base category. For the converse, we consider two cases. In the first case the base category is assumed to be adhesive and the morphism along which we take the lax pullback complement is admissible (i.e., its pushout along a monomorphism forms a pullback complement square), while in the second case the base category is -cohesive, however the morphism along which we take the lax pullback complement is an arbitrary total morphism. Finally as a byproduct we provide the connection between exponentials in the partial morphism category and its base category.
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