@article{article_339314, title={Morphism Properties of Digital Categories}, journal={Celal Bayar University Journal of Science}, volume={13}, pages={619–622}, year={2017}, DOI={10.18466/cbayarfbe.339314}, author={Öztunç, Simge}, keywords={Digital Image,Digital Category,monomorphism,epimorphism,isomorphism}, abstract={<p> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">In this paper we defined the </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify; position: relative; top: 6pt;"> <v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"> <o:lock v:ext="edit" aspectratio="t"> </o:lock> </v:path> </v:stroke> </v:shapetype> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:27.75pt; height:16.5pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz" o:title=""> </v:imagedata> </v:shape> </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">  </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">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 </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify; position: relative; top: 2pt;"> <v:shape id="_x0000_i1026" type="#_x0000_t75" style="width:22.5pt;height:11.25pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""> </v:imagedata> </v:shape> </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">  </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">adjacency relation. Hence we determined the initial and terminal objects of digital categories which have digital image with </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify; position: relative; top: 2pt;"> <v:shape id="_x0000_i1027" type="#_x0000_t75" style="width:22.5pt; height:11.25pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""> </v:imagedata> </v:shape> </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">  </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">adjacency as objects. </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">   </span> <span style="font-family: "Times New Roman", serif; font-size: 10pt; text-align: justify;">In addition to this we proved that the objects of the same type in a digital category are isomorphic. </span> <br> </p>}, number={3}, publisher={Manisa Celal Bayar Üniversitesi}