Colimits in the category of structural spaces and their realizations in fuzzy-type categories

[1] J. Adámek, H. Herrlich, G. E. Strecker, Abstract and concrete categories, John Wiley and Sons, New York, 1990. Republished in: Reprints in Theory and Applications of Categories, 17, 2006.

[2] M. Akbarpour, G. Mirhosseinkhani, Compactness and closed maps in topological fuzzes, Journal of Mathematical Extension,16(9) (2022), 1-11. https://doi.org/10.30495/JME.2022.1787

[3] N. Çağman, S. Enginoğlu, F. Çıtak, Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems, 8(3) (2011), 137-147. https://doi.org/10.22111/IJFS.2011.292

[4] N. Çağman, S. Karataş, S. Enginoğlu, Soft topology, Computers and Mathematics with Applications, 62(1) (2011), 351-358. https://doi.org/10.1016/j.camwa.2011.05.016

[5] M. K. Chakraborty, T. M. G. Ahsanullah, Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems, 45(1) (1992), 103-108. https://doi.org/10.1016/0165-0114(92)90096-M

[6] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24(1) (1968), 182-190. https://doi.org/10.1016/0022-247X(68)90057-7

[7] D. Çoker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88(1) (1997), 81-89. https://doi.org/10.1016/S0165-0114(96)00076-0

[8] N. Georgiou, A. C. Megaritis, Soft set theory and topology, Applied General Topology, 15(1) (2014), 93-109. https://doi.org/10.4995/agt.2014.2268

[9] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1) (1967), 145-174. https://doi.org/10.1016/0022-247X(67)90189-8

[10] J. A. Goguen, The fuzzy tychonoff theorem, Journal of Mathematical Analysis and Applications, 43(3) (1973), 734-742. https://doi.org/10.1016/0022-247X(73)90288-6

[11] S. N. Hosseini, R. Amini, Structural topology in a category, Iranian Journal of Fuzzy Systems, 18(6) (2021), 45-54. https://doi.org/10.22111/IJFS.2021.6332

[12] K. Hur, P. K. Lim, J. G. Lee, J. Kim, The category of neutrosophic sets, Neutrosophic Sets and Systems, 14(1) (2016), 12-20. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1167&context=nss journal

[13] B. Hutton, Products of fuzzy topological spaces, Topology and its Applications, 11(1) (1980), 59-67. https://doi.org/10.1016/0166-8641(80)90017-6

[14] S. Karataş, C. Kuru, Neutrosophic topology, Neutrosophic Sets and Systems, 13 (2016), 90-95. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1160&context=nss journal

[15] M. Z. Kazemi Baneh, S. N. Hosseini, Limits in the category of structural topological spaces, U.P.B. Scientific Bulletin, Series A: Applied Mathematics and Physics, 86(2) (2024), 55-70.

[16] A. Kharal, B. Ahmad, Mappings on fuzzy soft classes, Hindawi Publishing Corporation, Advances in Fuzzy Systems, (2009), 1-6. Article ID 407890. https://doi.org/10.1155/2009/407890

[17] A. Kharal, B. Ahmad, Mappings on soft classes, New Mathematics and Natural Computation, 7(3) (2011), 471-481. https://doi.org/10.1142/S1793005711002025

[18] F. G. Lupiánez, On neutrosophic topology, The International Journal of Systems and Cybernetics, Systems and Management Science, 37(6) (2008), 797-800. https://doi.org/10.1108/03684920810876990

[19] S. Mac Lane, I. Moerdijk, Sheaves in geometry and logic: A first introduction to topos theory, Universitext, Springer-Verlag, New York, 1992. https://doi.org/10.1007/978-1-4612-0927-0

[20] P. K. Maji, A. R. Roy, R. Biswas, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001), 589-602. https://sid.ir/paper/633097/en

[21] Gh. Mirhosseinkhani, N. Nazari, The category of topological De Morgan molecular lattices, Journal of Mathematical Extension, 14(3) (2020), 133-149. https://doi.org/10.30495/jme.v14i0.1127

[22] D. A. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4-5) (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5

[23] S. Y. Musa, B. A. Asaad, Hypersoft topological spaces, Neutrosophic Sets and Systems, 49 (2022), 397-415. https://doi.org/10.5281/zenodo.6426447

[24] S. E. Rodabaugh, Powerset operator foundations for poslat fuzzy set theories and topologies. In Mathematics of fuzzy sets: logic, topology and measure theory, U. Höhle and S. E. Rodabaugh, eds., The Handbooks of Fuzzy Sets Series, Dordrecht: Kluwer Academic Publishers, 3 (1999), 91-116. https://doi.org/10.1007/978-1-4615-5079-2 3

[25] S. Roy, T. K. Samanta, A note on fuzzy soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2) (2012), 305-311.

[26] M. Saeed, M. Ahsan, A. U. Rahman, A novel approach to mappings on hypersoft classes with application, Theory and Application of Hypersoft Set, (2021), 175-191. https://doi.org/10.5281/zenodo.4743384

[27] M. Saeed, M. Ahsan, M. Siddique, M. Ahmad, A study of the fundamentals of hypersoft set theory, International Journal of Scientific and Engineering Research, 11(1) (2020), 1-9. https://doi.org/10.5281/zenodo.6779593

[28] M. Saeed, A. Rahman, M. Ahsan, F. Smarandache, An inclusive study on fundamentals of hypersoft Set. In Theory and Application of Hypersoft Set, 2021 ed., F. Smarandache, M. Saeed, M. Abdel-Baset, M. Saqlain, Pons Publishing House: Brussels, Belgium, (2021), 1-23. https://doi.org/10.5281/zenodo.7361633

[29] A. A. Salama, S. A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Mathematics, 3(4) (2012), 31-35. https://doi.org/10.9790/5728-0343135

[30] A. A. Salama, F. Smarandache, V. Kromov, Neutrosophic closed set and neutrosophic continuous functions, Neu trosophic Sets and Systems, 4(1) (2014), 4-8. https://doi.org/10.5281/zenodo.30213

[31] M. Shabir, M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61(7) (2011), 1786-1799. https://doi.org/10.1016/j.camwa.2011.02.006

[32] F. Smarandache, Extension of soft set to hypersoft set, and then to plithogenic hypersoft set, Neutrosophic Sets and Systems, 22(1) (2018), 168-170.

[33] F. Smarandache, et. al., Proceedings of the first international conference on neutrosophy, neutrosophic logic, neu trosophic set, neutrosophic probability and statistics, University of New Mexico, Gallup, NM 87301, USA (2002). https://doi.org/10.48550/arXiv.math/0306384

[34] B. P. Varol, H. Aygün, Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics, 41(3) (2012), 407-419. https://izlik.org/JA73DG32JC

[35] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47(3) (1992), 351-376. https://doi.org/10.1016/0165-0114(92)90301-J

[36] H. Yavari, S. N. Hosseini, Topological molecular lattices as O-structural spaces, 53rd Annual Iranian Mathematics Conference, University of Science and Technology of Mazandaran, (2022), 902-905.

[37] H. Yavari, S. N. Hosseini, Limits in the category of O-structural spaces, 56th Annual Iranian Mathematics Confer ence, Vali-e-Asr University of Rafsanjan, (2025), 335-339.

[38] H. Yavari, S. N. Hosseini, Topologicality, completeness and cocompleteness of the category of structural spaces, Filomat, 40(8) (2026), 2997-3014. https://doi.org/10.2298/FIL2608997Y