Quotients of monodromy groupoids
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CitationMucuk, O., Şahan, T. (2019). Quotients of monodromy groupoids. International Conference of Mathematical Sciences. s. 030028(1)-030028(4).
The main object of this extended abstract is to define the quotient groupoid of the monodromy groupoid for a topological group-groupoid using the categorical assignment between crossed modules and group-groupoids and state some results without in detail. The idea of monoromy principle is that a local morphism f on a topological structure G is extended not only to G itself but also to some simply connected cover of G [12, Theorem 2, Chapter 2]. A version of this result was developed in  for Lie groups. The notion of monodromy groupoid was introduced by J. Pradines in a series of the works [27, 28, 29, 30] to generalize a standard construction of a simply connected Lie group from a Lie algebra to a corresponding construction of a Lie groupoid from a Lie algebroid (see also [16, 17, 18, 19, 25, 33]). For more discussions about holonomy and monodromy groupoids we refer the readers to  and . Let G be a topological groupoid. The monodromy groupoid denoted by Mon(G) is defined by Mackenzie in [17, p.67-70] as a disjoint union of the universal covers of the stars Gx’s. The topological aspect of the monodromy groupoid was developed in  using the holonomy technics of  and written in Lie groupoid case including topological groupoids in  and .
SourceInternational Conference of Mathematical Sciences
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