Abstract
In this paper the category, of partial morphisms of a category \(\mathcal{C}\) with respect to a certain class \(\mathcal{D}\) of subobjects of \(\mathcal{C}\) is formed and the universality of monomorphisms of \({\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\mathcal{C}} }\) is investigated. The main result characterizes \({\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\mathcal{C}} }\)-universality of monos, in terms of \(\mathcal{C}\)-universality of monos and the existence of local \(\mathcal{C}\)-implications.
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Adamek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories. John Wiley & Sons, Inc (1990) http://www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf
Asperti, A., Longo, G.: Categories Types and Structures. M.I.T. Press (1991)
Booth, P.I., Brown, R.: Spaces of partial maps, fibred mapping spaces and the compact-open topology. Gen. Topol. Appl. 8, 181–195 (1978)
Herrlich, H.: On the representability of partial morphisms in top and in related constructs. Springer Lect. Notes Math. 1348, 143–153 (1988)
Johnstone, P.T.: Topos Theory. Academic Press, London (1977)
Lowen, E., Lowen, R.: A Quasitopos containing CONV and MET as full subcategories. Int. J. Math. Math. Sci. 11(3), 41–438 (1988)
Maclane, S., Moerdijk, I.: Sheaves in Geometry and Logic, a First Introduction to Topos Theory. Springer-Verlag, New York (1992)
Menezes, P.B.: Diagonal compositionality of partial petri nets. Electr. Notes in Theor. Comp. Sci. 14, 274–301 (1998)
Mori, M., Kawahara, Y.: Rewriting fuzzy graphs. Department of Informatics. Kyushu University 33, Fukuoka 812-81, Japan (1997)
Palmgren, E., Vickers, S.J.: Partial horn logic and cartesian categories. U.U.D.M. Report 36, ISSN 1101-3591 (2005)
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Hosseini, S.N., Mielke, M.V. Universal Monos in Partial Morphism Categories. Appl Categor Struct 17, 435–444 (2009). https://doi.org/10.1007/s10485-007-9123-2
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DOI: https://doi.org/10.1007/s10485-007-9123-2