Yazar "Mucuk, Osman" seçeneğine göre listele

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    Crossed module aspects of monodromy groupoids for topological internal groupoids
    (American Institute Physics, 2019) Mucuk, Osman; Demir, Serap; Şahan, Tunçar
    In this extended abstract we state the topological version of categorical equivalence between internal groupoids and crossed modules in the category of groups with operations; and explain how to develop crossed module aspect of monodromy groupoids for topological internal groupoids.
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    Crossed modules, double group-groupoids and crossed squares
    (University of Nis, 2020) Temel, Sedat; Şahan, Tunçar; Mucuk, Osman
    The purpose of this paper is to obtain the notion of crossed module over group-groupoids con-sidering split extensions and prove a categorical equivalence between these types of crossed modules and double group-groupoids. This equivalence enables us to produce various examples of double groupoids. We also prove that crossed modules over group-groupoids are equivalent to crossed squares.
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    From cssc-crossed modules to categorical groups
    (Tbilisi Centre for Mathematical Sciences, 2024) Datuashvili, Tamar; Mucuk, Osman; Alemdar, Nazmiye; Şahan, Tunçar
    For any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is associated, this construction will enable us to prove an equivalence between the categories of categorical groups and of cssc-crossed modules in the sequel to this paper.
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    Group-groupoid actions and liftings of crossed modules
    (Walter de Gruyter GmbH, 2019) Mucuk, Osman; Şahan, Tunçar
    The aim of this paper is to define the notion of lifting via a group morphism for a crossed module and give some properties of this type of liftings. Further, we obtain a criterion for a crossed module to have a lifting crossed module. We also prove that the category of the lifting crossed modules of a certain crossed module is equivalent to the category of group-groupoid actions on groups, where the group-groupoid corresponds to the crossed module. © 2018 Walter de Gruyter GmbH, Berlin/Boston.
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    Group-groupoids and crossed module aspects of monodromy groupoids
    (American Institute Physics, 2019) Mucuk, Osman; Demir, Serap; Şahan, Tunçar
    In this extended abstract considering the topological version of categorical equivalence of crossed modules and group-groupoids we develop crossed module aspects of monodromy group-groupoids for topological group-groupoids and give some examples for monodromy groupoids. © 2019 Author(s).
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    Groups up to congruence relation and from categorical groups to c-crossed modules
    (Springer Science and Business Media Deutschland GmbH, 2020) Datuashvili, Tamar; Mucuk, Osman; Şahan, Tunçar
    We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to a c-group and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.
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    Internal groupoid actions and liftings of crossed modules within groups with operations
    (American Institute Physics, 2019) Akız, Hürmet Fulya; Mucuk, Osman; Şahan, Tunçar
    In this extended abstract we define the notion of lifting of a crossed module in groups with operations and state some properties of this type of liftings. Furthermore for a certain crossed module we give a categorical equivalence between the lifting of crossed modules and internal groupoid actions in groups with operations. © 2019 Author(s).
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    Liftings of crossed modules in the category of groups with operations
    (Boletim da Sociedade Paranaense de Matematica, 2020) Fulya Akız, Hürmet; Mucuk, Osman; Şahan, Tuncar
    In this paper we define the notion of lifting of a crossed module via the morphism in groups with operations and give some properties of this type of liftings. Further we prove that the lifting crossed modules of a certain crossed module are categorically equivalent to the internal groupoid actions on groups with operations, where the internal groupoid corresponds to the crossed module.
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    Normality and quotient in the category of crossed modules within the category of groups with operations
    (Boletim da Sociedade Paranaense de Matematica, 2020) Şahan, Tunçar; Mucuk, Osman
    In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and then give some properties of such crossed modules in groups with operations.
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    Normality and quotient of crossed modules within group with operations
    (American Institute Physics, 2019) Şahan, Tunçar; Mucuk, Osman
    In this note we define the notions of normal subcrossed module and quotient crossed module within groups with opera-tions; and give same results on these crossed modules. © 2019 Author(s).
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    Quotients of monodromy groupoids
    (American Institute Physics, 2019) Mucuk, Osman; Şahan, Tunçar
    In this note we explain how to develop the quotient groupoid of the monodromy groupoid for given a topological group-groupoid using crossed modules. © 2019 Author(s).