Skip to main content
Log in

Pullback in Partial Morphism Categories

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

In this article we give necessary and sufficient conditions for the existence of a pullback of a two sink, in a partial morphism category.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Adamek, J., Herrlich, H., Strecker, G.E.: Abstract and concrete categories. Wiley, New York (1990). http://www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf

    MATH  Google Scholar 

  2. Asperti, A., Longo, G.: Categories Types and Structures. MIT Press, Cambridge, MA (1991)

    MATH  Google Scholar 

  3. Booth, P.I., Brown, R.: Spaces of partial maps, fibred mapping spaces and the compact-open topology. Gen. Topol. Appl. 8, 181–195 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  4. Corradini, A., Heindel, T., Hermann, F., König, B.: Sesqui-pushout Rewriting. In: Corradini, A., et al. (eds.) ICGT 2006, LNCS 4178, pp 30–45 (2006)

  5. Dyckhoff, R., Tholen, W.: Exponentiable morphisms, partial products and pullback complements. J. Pure Appl. Algebra 49, 103–116 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Herrlich, H.: On the Representability of Partial Morphisms in Top and in Related Constructs. Springer Lect. Notes Math., vol. 1348, pp 143–153 (1988)

  7. Hosseini, S.N., Mielke, M.V.: Universal monos in partial morphism categories. Appl. Categ. Struct. 17, 435–444, (2009). doi:10.1007/s10485-007-9123-2

    Article  MathSciNet  MATH  Google Scholar 

  8. Hosseini, S.N., Shir Ali Nasab, A.R.: Finite Products in Partial Morphism Categories. Theory Appl. Categ. 29(10), 302–314 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Hosseini, S. N., Shir Ali Nasab, A. R.: Equalizers in Partial Morphism Categories, submitted

  10. Johnstone, P.T.: Topos Theory. Academic Press, New York (1977)

    MATH  Google Scholar 

  11. Lowen, E., Lowen, R.: A quasitopos containing CONV and MET as full subcategories. Int. J. Math. Math. Sci. 11(3), 41–438 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mac Lane, S., Moerdijk, I.: Sheaves in geometry and logic. A First Introduction to Topos Theory. Springer, New York (1992)

    Google Scholar 

  13. Menezes, P.B.: Diagonal Compositionality of Partial Petri Nets. Electronic Notes in Theoretical Computer Science, p 14 (1998)

  14. Mori, M., Kawahara, Y.: Rewriting Fuzzy Graphs, Department of Informatics, Kyushu University 33, Fukuoka 812–81, Japan (1997)

  15. Palmgren, E., Vickers, S.J.: Partial Horn Logic and Cartesian Categories, U.U.D.M. Report 36, ISSN 1101–3591 (2005)

  16. Shir Ali Nasab, A.R., Hosseini, S.N.: Partial pullback complement rewriting. Theor. Comput. Sci. 594, 44–64 (2015). doi:10.1016/j.tcs.2015.04.006

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. N. Hosseini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shir Ali Nasab, A.R., Hosseini, S.N. Pullback in Partial Morphism Categories. Appl Categor Struct 25, 197–225 (2017). https://doi.org/10.1007/s10485-015-9420-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-015-9420-0

Keywords

Mathematics Subject Classifications (2010)

Navigation