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Closed Model Category Structures
2010By a closed model category we mean a model category in the sense of Hovey [49]. The closed model categories that we will construct are also abelian model categories in the sense of [51], so our results can be viewed as particular cases of the general framework developed in [50].
Leonid Positselski +2 more
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Closed model categories for the n-type of spaces and simplicial sets
Mathematical Proceedings of the Cambridge Philosophical Society, 1995AbstractFor each integer n ≥ 0, we give a distinct closed model category structure to the categories of spaces and of simplicial sets. Recall that a non-empty map is said to be a weak equivalence if it induces isomorphisms on the homotopy groups for any choice of base point.
Elvira-Donazar, Carmen +1 more
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Categories with homotopy determine a closed model structure
Journal of Mathematical Sciences, 2008In a category with homotopy $$\mathfrak{K}$$ (Definition 1.1), one can define a natural concept of (co)fibrations and weak equivalences (Sec. 2) such that some properties of a closed model category hold. If
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On closed models on the precategory of small categories and simplicial schemes
Russian Mathematical Surveys, 1984Denote by Cat the category of small categories and by proCat the corresponding procategory. In a previous paper, the author had constructed a homotopy theory in Cat. The paper under review translates the notions of weak equivalence, fibration and cofibration into proCat, which is shown to be a closed model category in the sense of \textit{D. G. Quillen}
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On the simple object associated to a diagram in a closed model category
Mathematical Proceedings of the Cambridge Philosophical Society, 1986In this paper we develop a descent technique for generalized (co)-homology theories defined in the category of algebraic varieties. By such a theory we mean a functor Sch→C, where C is a closed model category in the sense of Quillen satisfying certain axioms (cf. §4).
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A version of an E 2 closed model category structure
1996Let X • be a pointed simplicial set. Its constant bisimplicial extension cX •• can be thought of as a resolution of X • by the zero spheres in the following sense: 1) by “flipping the axes”, cX • • can be seen as a simplicial object having in each degree a wedge of zero spheres; 2) the diagonal Δ(cX • •) is isomorphic to X •.
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A cartesian-closed category for higher-order model checking
2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2017Martin Hofmann, Jeremy Ledent
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kPAM 2.0: Feedback Control for Category-Level Robotic Manipulation
IEEE Robotics and Automation Letters, 2021Wei Gao
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