We study orbifolds and strong maps of orbifolds. We begin with introducing a representation
for orbifolds that consists of internal categories in the category of topological
spaces. These categories are built from atlas charts and chart embeddings without
equivalence relation. They represent orbifolds and atlas maps, but do not work well
for general strong maps. We generalize the notion of category of fractions to internal
categories in the category of topological spaces. We find its universal property for an
internal category in the category of topological spaces. We apply this to the atlas category
to obtain an atlas groupoid. We give a description of strong maps of orbifolds
and the equivalence relation on them in terms of atlas groupoids. We define paths in
orbifolds as strong maps. We use our construction to give an explicit description of
the equivalence classes on such paths in terms of charts and chart embeddings.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:NSHD.ca#10222/21458 |
| Date | 12 March 2013 |
| Creators | Sibih, Alanod |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
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