Simplicial Localization ! 3 of Categories
نویسنده
چکیده
1.1. The simplicial localization. The localization of a category C with respect to a subcategory W is the category C[W-‘1 which has the same objects as C and is obtained from C by formally inverting the maps of W. Our purpose here is to show that C[W-‘1 reflects just one aspect of a much richer object, the simplicial localization LC. This simplicial localization LC is a simplicial category with in each dimension the same objects as C (i.e. for every two objects X, YE C, the maps X + YE LC form a simplicial set LC(X, Y)), which has the localization C[W-‘1 as its “category of components”. By this we mean that, for every two objects X, YE C,
منابع مشابه
Summer 2016 Homotopy Theory Seminar
1. Simplicial Localizations and Homotopy Theory: 5/24/16 1 2. Simplicial Sets: 5/31/16 3 3. Model Categories: 6/7/16 8 4. Localization: Classical and Bous eld: 6/17/16 12 5. Simplicial Localizations of Categories: 6/21/16 16 6. The Hammock Localization: 6/28/16 20 7. The Indexing Category II: 7/8/16 21 8. Homotopy Calculi of Fractions and You!: 7/19/16 24 9. The Grothendieck Construction: 7/26/...
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