Fundamental groupoid of Alexandroff space X is naturally isomorphic to localization of its thin specialization-preorder category; regular coverings are represented by morphism-inverting functors extending Minian-Barmak.
$G$-colorings of posets, coverings and presentations of the fundamental group
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We introduce the notion of a coloring of a poset, which consists of a labeling of the edges in its Hasse diagram by elements in a given group $G$. We use $G$-colorings to describe the covering maps of posets and present a new method based on colorings to obtain concrete and simple presentations of the fundamental group of polyhedra.
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2019 1verdicts
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Regular coverings and fundamental groupoids of Alexandroff spaces
Fundamental groupoid of Alexandroff space X is naturally isomorphic to localization of its thin specialization-preorder category; regular coverings are represented by morphism-inverting functors extending Minian-Barmak.