Morphism Properties of Digital Categories

Yıl 2017, , 619 - 622, 30.09.2017

Simge Öztunç

https://doi.org/10.18466/cbayarfbe.339314

Öz

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.

Anahtar Kelimeler

Digital Image, Digital Category, monomorphism, epimorphism, isomorphism

Kaynakça

• 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.