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Morphism Properties of Digital Categories

Year 2017, Volume: 13 Issue: 3, 619 - 622, 30.09.2017
https://doi.org/10.18466/cbayarfbe.339314

Abstract

In this paper we defined the



















 category and researched
the properties of monomorphism, epimorphism and isomorphism for digital
categories which are related with the categorical structure in [1]. Also
initial and terminal objects in digital categories are defined by using


 adjacency relation.
Hence we determined the initial and terminal objects of digital categories
which have digital image with


 adjacency as
objects.
   In addition to this we proved
that the objects of the same type in a digital category are isomorphic.

References

  • 1. Öztunç S., Mutlu A., Categories in Digital Images, American Journal of Mathematics and Statistics, January 2013;Vol.3, No.1.
  • 2. Rosenfeld A., ‘Continuous’ functions on digital pic-tures, Pattern Recognition Letters, 1986; Vol. 4, 177–184.
  • 3. Han, S.E. An Extended Digital 01 (k0,k1 )-Continuity. J. Appl. Math. Comput. 2004, 16, 445-452.
  • 4. Kong T.Y., Roscoe A.W., and Rosenfeld A., Concepts of digital topology, Topology and its Applications, 1992, 46, 219–262.
  • 5. Boxer L., Digitally continuous functions, Pattern Recognition Letters, 1994, 15 833–839.
  • 6. Boxer L., Properties of Digital Homotopy, Journal of Mathematical Imaging and Vision, 2005, 22 19–26.
  • 7. Karaca I., Boxer L. and Öztel A., Topological Invari-ants in Digital Images, Jour. of Mathematical Sciences: Advances and Applications, 2011, 2, 109-140.
  • 8. Awoday S., Category Theory, Oxford Science Publica-tion, 2010.
  • 9. Blyth T.S., Categories, Longman 1986.
  • 10. Öztunç S., Some Properties of Soft Categories, Interna-tional Journal of Modeling and Optimization, 2016; 6(2),91-95.
Year 2017, Volume: 13 Issue: 3, 619 - 622, 30.09.2017
https://doi.org/10.18466/cbayarfbe.339314

Abstract

References

  • 1. Öztunç S., Mutlu A., Categories in Digital Images, American Journal of Mathematics and Statistics, January 2013;Vol.3, No.1.
  • 2. Rosenfeld A., ‘Continuous’ functions on digital pic-tures, Pattern Recognition Letters, 1986; Vol. 4, 177–184.
  • 3. Han, S.E. An Extended Digital 01 (k0,k1 )-Continuity. J. Appl. Math. Comput. 2004, 16, 445-452.
  • 4. Kong T.Y., Roscoe A.W., and Rosenfeld A., Concepts of digital topology, Topology and its Applications, 1992, 46, 219–262.
  • 5. Boxer L., Digitally continuous functions, Pattern Recognition Letters, 1994, 15 833–839.
  • 6. Boxer L., Properties of Digital Homotopy, Journal of Mathematical Imaging and Vision, 2005, 22 19–26.
  • 7. Karaca I., Boxer L. and Öztel A., Topological Invari-ants in Digital Images, Jour. of Mathematical Sciences: Advances and Applications, 2011, 2, 109-140.
  • 8. Awoday S., Category Theory, Oxford Science Publica-tion, 2010.
  • 9. Blyth T.S., Categories, Longman 1986.
  • 10. Öztunç S., Some Properties of Soft Categories, Interna-tional Journal of Modeling and Optimization, 2016; 6(2),91-95.
There are 10 citations in total.

Details

Journal Section Articles
Authors

Simge Öztunç

Publication Date September 30, 2017
Published in Issue Year 2017 Volume: 13 Issue: 3

Cite

APA Öztunç, S. (2017). Morphism Properties of Digital Categories. Celal Bayar University Journal of Science, 13(3), 619-622. https://doi.org/10.18466/cbayarfbe.339314
AMA Öztunç S. Morphism Properties of Digital Categories. CBUJOS. September 2017;13(3):619-622. doi:10.18466/cbayarfbe.339314
Chicago Öztunç, Simge. “Morphism Properties of Digital Categories”. Celal Bayar University Journal of Science 13, no. 3 (September 2017): 619-22. https://doi.org/10.18466/cbayarfbe.339314.
EndNote Öztunç S (September 1, 2017) Morphism Properties of Digital Categories. Celal Bayar University Journal of Science 13 3 619–622.
IEEE S. Öztunç, “Morphism Properties of Digital Categories”, CBUJOS, vol. 13, no. 3, pp. 619–622, 2017, doi: 10.18466/cbayarfbe.339314.
ISNAD Öztunç, Simge. “Morphism Properties of Digital Categories”. Celal Bayar University Journal of Science 13/3 (September 2017), 619-622. https://doi.org/10.18466/cbayarfbe.339314.
JAMA Öztunç S. Morphism Properties of Digital Categories. CBUJOS. 2017;13:619–622.
MLA Öztunç, Simge. “Morphism Properties of Digital Categories”. Celal Bayar University Journal of Science, vol. 13, no. 3, 2017, pp. 619-22, doi:10.18466/cbayarfbe.339314.
Vancouver Öztunç S. Morphism Properties of Digital Categories. CBUJOS. 2017;13(3):619-22.