On the loop space of a 2-category
Every small category C has a classifying space BC associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper, we study the classifying space B2C of a 2-category C and prove that,...
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| Formato: | Artículo publishedVersion |
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2012
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224049_v216_n1_p28_delHoyo https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00224049_v216_n1_p28_delHoyo_oai |
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| Sumario: | Every small category C has a classifying space BC associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper, we study the classifying space B2C of a 2-category C and prove that, under certain conditions, the loop space ΩcB2C can be recovered up to homotopy from the endomorphisms of a given object. We also present several subsidiary results that we develop to prove our main theorem. © 2011 Elsevier B.V. |
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