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Universal homotopy theories | Daniel Dugger
; | Date: |
11 Jul 2000 | Subject: | Algebraic Topology; Category Theory | math.AT math.CT | Affiliation: | Purdue University | Abstract: | Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations’ into these universal gadgets. The paper develops this formalism and discusses various applications, for instance to the study of homotopy colimits, the Dwyer-Kan theory of framings, and to the homotopy theory of schemes. | Source: | arXiv, math.AT/0007070 | Services: | Forum | Review | PDF | Favorites |
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