Abstract
The paper gives a sufficient condition for the existence of all pushouts in an arbitrary category of partial maps \(\mathbb{C}_{*\mathcal{M}}\) that is necessary whenever the category of total maps \(\mathbb{C} \subseteq \mathbb{C}_{*\mathcal{M}}\) has cocones of spans; the latter is the case in all slice categories of ℂ and thus the condition is necessary locally. The main theorem is that, given an admissible class of monos \(\mathcal{M}\) in a category ℂ that has cocones of spans, the category of partial maps \(\mathbb{C}_{*\mathcal{M}}\) has pushouts if and only if the category of total maps ℂ has hereditary pushouts and right adjoints to inverse image functors (where both properties are w.r.t. \(\mathcal{M}\)). This result clarifies previous work by Kennaway on graph rewriting in categories of partial maps that implicitly assumed existence of cocones of spans in the category of total maps.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.