Lifting homotopy T-algebra maps to strict maps |
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Authors: | Niles Johnson Justin Noel |
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Institution: | 1. The Ohio State University Newark, 1179 University Drive, Newark, OH 43055, USA;2. Universität Regensburg, Universitätsstr. 31, Regensburg D-93040, Germany |
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Abstract: | The settings for homotopical algebra—categories such as simplicial groups, simplicial rings, A∞ spaces, E∞ ring spectra, etc.—are often equivalent to categories of algebras over some monad or triple T. In such cases, T is acting on a nice simplicial model category in such a way that T descends to a monad on the homotopy category and defines a category of homotopy T-algebras. In this setting there is a forgetful functor from the homotopy category of T-algebras to the category of homotopy T-algebras. |
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Keywords: | primary 55P99 55S35 secondary 13D03 18C15 18C10 18G55 55P43 55P62 55T05 55Q50 |
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