43 citations · 145 across the 12 of their papers we have counts for
12 papers
Pentactions and action representability in the category of reduced groups with action
Tamar Datuashvili, Tunçar Şahan
A notion of pentaction of any object in the category of reduced groups with action is introduced. The operations are defined in the set $\mathsf{Pentact}(A…
Actions and semi-direct products in categories of groups with action
Tamar Datuashvili, Tunçar Şahan
Derived actions in the category of groups with action on itself are defined and described. This category plays a crucial role in the solution of Loday's two…
Groups up to congruence relation and from categorical groups to c-crossed modules
Tamar Datuashvili, Osman Mucuk, Tunçar Şahan
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) ar…
Further remarks on liftings of crossed modules
Tunçar Şahan
In this paper we define the notion of pullback lifting of a lifting crossed module over a crossed module morphism and interpret this notion in the category of group-groupoid action…
Actions of internal groupoids in the category of Leibniz algebras
Tunçar Şahan, Ayhan Erciyes
The aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate the properties of well-known notions such as…
Coverings of internal groupoids and crossed modules in the category of groups with operations
H. Fulya Akız, Nazmiye Alemdar, Osman Mucuk +1
In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.
Covering groupoids of categorical groups
Osman Mucuk, Tunçar Şahan
If is a topological group, then its fundamental groupoid is a group-groupoid which is a group object in the category of groupoids. Further if is a path connected top…
Group-groupoid actions and liftings of crossed modules
Osman Mucuk, Tunçar Şahan
The aim of this paper is to define the notion of lifting of a crossed module via a group morphism and give some properties of this type of the lifting. Further we obtain a criterio…
Normality and quotient in crossed modules, cat-groups and internal groupoids within groups with operations
Tunçar Şahan, Osman Mucuk
In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and using the equivalence of crossed modules over groups…
Coverings and crossed modules of topological groups with operations
Osman Mucuk, Tunçar Şahan
It is a well known result in the covering groups that a subgroup of the fundamental group at the identity of a semi-locally simply connected topological group determines a cove…
Group-groupoids and monodromy groupoids
Osman Mucuk, Berrin Kılıçarslan, Tunçar Şahan +1
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
On G-Sequential Continuity
Osman Mucuk, Tunçar Şahan
Let be a first countable Hausdorff topological group. The limit of a sequence in defines a function denoted by from the set of all convergence sequences to . This…