Categorical structures of soft groups
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METHODOLOGIES AND APPLICATION
Categorical structures of soft groups Simge Öztunç1 · Sedat Aslan1 · Hemen Dutta2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In the current paper, the category of soft groups and soft group homomorphisms is constructed and it is proved that this structure satisfies the category conditions. Also, algebraic properties of some types of soft group morphisms are obtained. Finally, an application is presented as ‘cube’ of soft groups and soft group homomorphisms. Keywords Soft group category · Soft monomorphism · Soft epimorphism · Soft isomorphism
1 Introduction The theory of soft set is progressing rapidly as a new subject of mathematics which is propounded by Molodtsov (1999) in 1999. Soft sets have many applications in different areas, especially engineering, physics, medicine and economics. Also, it has significant theoretical properties which are studied in Aras and Po¸sul (2016), Aygunoglu and Aygun (2012), Chen et al. (2005), Gulistan et al. (2018), Maji et al. (2003), Shabir and Naz (2011) and Tanay and Kandemir (2011). Moreover, soft set theory is an alternative to set theory as a fortification for mathematics researchers. The concept of soft groups and soft homomorphism was given in Aktas and Cagman (2007), further properties were investigated in Yaylalı Umul et al. (2019), and soft sets and soft rings were investigated in Acar et al. (2010). Further properties that deal with soft topological groups and rings are contained in Shah and Shaheen (2014). Other details Communicated by V. Loia.
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Simge Öztunç [email protected] Sedat Aslan [email protected] Hemen Dutta [email protected]
1
Department of Mathematics, Faculty of Arts and Science, Manisa Celal Bayar University, Martyr Prof. Dr. ˙Ilhan Varank Campus, 45030 Yunus Emre Manisa, Turkey
2
Department of Mathematics, Gauhati University, Gawahati, Assam 781014, India
for soft algebraic structures are included in Koyuncu and Tanay (2016). Also, continuity of soft mappings was investigated by Aras and Çakallı (2013) and Zorlutuna and Çakır (2015). On the other hand, category theory is multidisciplinary subject of mathematics which enables the transformation of different structures. It has come to hold a pivotal status in contemporary mathematics and theoretical computer science. Loosely, it is a plenary mathematical theory of structures and systems of structures. Soft category theory was searched out by Sardar and Gupta (2013), by Zahiri (2013) in 2013 and by Zhou et al. (2014) in 2014. After all, Öztunç (2016) has examined the properties of soft categories and Öztunç et al. (2017) have studied on monomorphism and epimorphism properties of soft categories. Also, O˘guz et al. (2019) investigated some properties of soft topological categories and Bayramov (2015) obtained some important results on singular homology theory of soft topological spaces. Further results for simplicial groups can be found in Mutlu and Porter (2001) and Mutlu and Porter (1998). In the current manuscript,
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