Boris Chorny
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Registered User
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I work in Algebraic Topology. My research interests include Homotopy theory, Homotopical Algebra, Calculus of Functors, Category Theory.
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2d |
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Homotopy left-exactness of a left derived functor If your model categories are simplicial or have some other homotopy meaningful enrichment, then homotopy limits may be viewed as weighted limits with a projective-cofibrant contractible diagram of weights. If the preservation of finite limits extends to the preservation of cotensors with finite simplicial sets, then finite homotopy limits are preserved over diagrams with a finite cofibrant replacement of $\ast$. |
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Apr 30 |
answered | uniqueness of $f$-localization |
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Feb 14 |
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The Quillen model structure on simplicial sets as a Bousfield localization You are welcome! I enjoyed thinking about your question. |
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Feb 14 |
accepted | The Quillen model structure on simplicial sets as a Bousfield localization |
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Feb 12 |
answered | The Quillen model structure on simplicial sets as a Bousfield localization |
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Feb 11 |
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Is there a notion of a “model category which admits left Bousfield localization?” Previous comment continued. Before we have a bunch of counterexamples of different nature we have no chance to classify model categories which admit Bousfield localizations. |
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Feb 11 |
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Is there a notion of a “model category which admits left Bousfield localization?” @Fernando: Thanks! I held myself back for quite a long time, but the temptation to join had finally overcome. @David: I have a comment on your third question. I do not know many examples, where the localization does not exist. In fact, the only example that comes to mind (apparently, I learned it from Bill Dwyer) is the following: Consider the category of pointed simplicial sets with the trivial model structure, then the localization with respect to the class of all weak equivalences does not exist, since homotopy is not concrete. |
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Feb 11 |
awarded | ● Supporter |
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Feb 10 |
awarded | ● Teacher |
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Feb 10 |
answered | Is there a notion of a “model category which admits left Bousfield localization?” |
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Jan 14 |
awarded | ● Autobiographer |
