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Dendroidal Spaces and ∞-Operads
Recall that a dendroidal set X is an ∞-operad if it satisfies the inner Kan condition; i.e., it has the extension property with respect to all inner...
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Depth and Simplicity of Ohkawa’s Argument
This is an expository article about Ohkawa’s theorem stating that acyclic classes of representable homology theories form a set. We provide...
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Complete Boolean Algebras are Bousfield Lattices
Given a complete Heyting algebra, we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given...
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Relative Categories
In Section 5.3 we saw that given a category with weak equivalences, it is possible to perform a...
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New Models from Old Ones
Suppose we have a category \(\mathcal {C}\)...
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Gluing compactly generated t-structures over stalks of affine schemes
We show that compactly generated t-structures in the derived category of a commutative ring R are in a bijection with certain families of compactly...
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Dendroidal Sets
In the previous chapters, we developed various models for \((\infty ,1)\)...
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Spectra
This chapter will be dedicated to model structures whose homotopy category is equivalent to the stable homotopy category, whose objects can be...
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A Whitehead theorem for periodic homotopy groups
We show that v n -periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes.
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Model Structures on the Category of Simplicial Sets
In this chapter we will apply the formalism of Quillen model categories discussed in the previous chapter to the category of simplicial sets. In his...
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Equivariant chromatic localizations and commutativity
In this paper, we study the extent to which Bousfield and finite localizations relative to a thick subcategory of equivariant finite spectra preserve...
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\(C^*\) -Algebras
The final chapter of Hovey’s book is entitled Vistas, and it outlines several questions of interest in the field of model categories [187, Chapter...
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Simplicial Operads and ∞-Operads
In this final chapter we fulfil one of the main promises of this book, namely we prove that the homotopy theory of ∞-operads is equivalent to that of...
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Chain Complexes
In this chapter, we will be concerned with the homotopy theory of bounded and unbounded chain complexes valued in a suitable abelian category...
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Three Model Structures on the Category of Dendroidal Sets
In this chapter we will construct several model structures on the category of dendroidal sets. For the different model structures, the fibrant...