منابع مشابه
Monoidal Model Categories
A monoidal model category is a model category with a closed monoidal structure which is compatible with the model structure. Given a monoidal model category, we consider the homotopy theory of modules over a given monoid and the homotopy theory of monoids. We make minimal assumptions on our model categories; our results therefore are more general, yet weaker, than the results of [SS97]. In part...
متن کاملSplitting Monoidal Stable Model Categories
If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S, S] . An idempotent e of this ring will split the homotopy category: [X,Y ] ∼= e[X,Y ]⊕(1−e)[X,Y ] . We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that i...
متن کاملOn Monoidal Equivalences and Ann-equivalences
The equivalence between a monoidal category and a strict one has been proved by some authors such as Nguyen Duy Thuan [8], Christian Kassel [2], Peter Schauenburg [7]. In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M -functors and M morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic chara...
متن کاملBousfield Localization of Monoidal Model Categories
I do my research in the context of model categories, sometimes specializing to the category Spectra in particular. I want to be able to apply algebraic ideas and methods to these categories, and I do so by replacing algebraic concepts by their categorical analogs. Every talk I give includes diagrams defining a ring object in a category. My research tends to be of the flavor: take some cool thin...
متن کاملAutonomization of Monoidal Categories
We define the free autonomous category generated by a monoidal category and study some of its properties. From a linguistic perspective, this expands the range of possible models of meaning within the distributional compositional framework, by allowing nonlinearities in maps. From a categorical point of view, this provides a factorization of the construction in [Preller and Lambek, 2007] of the...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2003
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2003.3.287