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:: Volume 13, Issue 3 (3-2024) ::
JGST 2024, 13(3): 29-39 Back to browse issues page
Category theory as a mathematical framework in spatial analysis; Challenges and opportunities
Abouzar Ramezani *
Abstract:   (307 Views)
Category theory is a branch of mathematics that is used to abstractly describe structures in mathematics. Unlike set theory, category theory focuses on relationships between objects, not on objects. Solving complexity in many engineering fields has become possible by structuring these problems on mathematical frameworks. Therefore, many researches have been conducted in the field of building complex problems on various branches of mathematics. In Geospatial information systems, mathematical sciences including set theory, graph theory and topology have been used, and category theory has been proposed as a new branch of mathematics to solve spatial problems. The purpose of this research is to investigate the opportunities and challenges that the category theory has created for the Geospatial information system in order to provide researchers with a more open view to use this framework in structuring spatial problems.
 
Article number: 3
Keywords: Category Theory, Mathematical Framework, Spatial Analysis, Topology
Full-Text [PDF 557 kb]   (165 Downloads)    
Type of Study: Tarviji | Subject: GIS
Received: 2023/08/1
References
1. Awodey, S., Category theory. 2010: Oxford university press.
2. Usery, E.L., Category theory and the structure of features in geographic information systems. Cartography and Geographic information systems, 1993. 20(1): p. 5-12. [DOI:10.1559/152304093782616751]
3. Fokkinga, M.M., Calculate categorically! Formal Aspects of Computing, 1992. 4: p. 673-692. [DOI:10.1007/BF03180568]
4. Rydeheard, D.E. and R.M. Burstall, Computational category theory. Vol. 152. 1988: Prentice Hall Englewood Cliffs.
5. Leinster, T., Basic category theory. Vol. 143. 2014: Cambridge University Press. [DOI:10.1017/CBO9781107360068]
6. Johnstone, P.T., Topos theory. 2014: Courier Corporation.
7. MacLane, S. and I. Moerdijk, Sheaves in geometry and logic: A first introduction to topos theory. 2012: Springer Science & Business Media.
8. Rousseau, C. Topos theory and complex analysis. in Applications of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, July 9-21, 1977. 2006. Springer.
9. Caramello, O. The unification of mathematics via topos theory. in Logic in Question: Talks from the Annual Sorbonne Logic Workshop (2011-2019). 2023. Springer. [DOI:10.1007/978-3-030-94452-0_30]
10. Lemin, A.J. Spectral decomposition of ultrametric spaces and topos theory. in Topology Proc. 2002. [DOI:10.1007/978-1-4612-1370-3_13]
11. McLarty, C., The uses and abuses of the history of topos theory. The British Journal for the Philosophy of Science, 1990. 41(3): p. 351-375. [DOI:10.1093/bjps/41.3.351]
12. Corcoran, P. and C.B. Jones, Topological data analysis for geographical information science using persistent homology. International Journal of Geographical Information Science, 2023. 37(3): p. 712-745. [DOI:10.1080/13658816.2022.2155654]
13. Bouchaffra, D., et al. Land Cover Change Detection based on Homology Theory. in 2019 6th International Conference on Image and Signal Processing and their Applications (ISPA). 2019. IEEE. [DOI:10.1109/ISPA48434.2019.8966911]
14. Pereira, C.M. and R.F. de Mello, Persistent homology for time series and spatial data clustering. Expert Systems with Applications, 2015. 42(15-16): p. 6026-6038. [DOI:10.1016/j.eswa.2015.04.010]
15. Xing, J., et al., A spatiotemporal brain network analysis of alzheimer's disease based on persistent homology. Frontiers in aging neuroscience, 2022. 14: p. 788571. [DOI:10.3389/fnagi.2022.788571]
16. Hu, L. and J. Wang. Geo-ontology integration based on category theory. in 2010 International Conference On Computer Design and Applications. 2010. IEEE.
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Ramezani A. Category theory as a mathematical framework in spatial analysis; Challenges and opportunities. JGST 2024; 13 (3) : 3
URL: http://jgst.issgeac.ir/article-1-1156-en.html


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Volume 13, Issue 3 (3-2024) Back to browse issues page
نشریه علمی علوم و فنون نقشه برداری Journal of Geomatics Science and Technology