Topology and Higher-Dimensional Category Theory: the Rough Idea

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dc.creatorLeinster, Tom
dc.date2001-06-27
dc.date.accessioned2026-07-07T04:42:21Z
dc.date.available2026-07-07T04:42:21Z
dc.descriptionHigher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the higher-dimensional diagrams one draws to represent these structures can be taken quite literally as pieces of topology. Examples of this are the braids in a braided monoidal category, and the pentagon which appears in the definitions of both monoidal category and A_infinity space. I will try to give a Friday-afternoonish description of some of the dreams people have for higher-dimensional category theory and its interactions with topology. Grothendieck, for instance, suggested that tame topology should be the study of n-groupoids; others have hoped that an n-category of cobordisms between cobordisms between ... will provide a clean setting for TQFT; and there is convincing evidence that the whole world of n-categories is a mirror of the world of homotopy groups of spheres.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0106240
dc.identifierhttp://arxiv.org/abs/math/0106240
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61745
dc.subjectCategory Theory
dc.subjectAlgebraic Topology
dc.subjectQuantum Algebra
dc.titleTopology and Higher-Dimensional Category Theory: the Rough Idea
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