1,005 research outputs found
Axiomatic homotopy theory for operads
We give sufficient conditions for the existence of a model structure on
operads in an arbitrary symmetric monoidal model category. General invariance
properties for homotopy algebras over operads are deduced.Comment: 29 pages, revised for publicatio
A cubical model for a fibration
In the paper the notion of truncating twisting function from a
simplicial set to a cubical set and the corresponding notion of twisted
Cartesian product of these sets are introduced. The latter
becomes a cubical set whose chain complex coincides with the standard twisted
tensor product . This construction together with
the theory of twisted tensor products for homotopy G-algebras allows to obtain
multiplicative models for fibrations.Comment: 15 pages, 1 figur
Motivic homotopy theory of group scheme actions
We define an unstable equivariant motivic homotopy category for an algebraic
group over a Noetherian base scheme. We show that equivariant algebraic
-theory is representable in the resulting homotopy category. Additionally,
we establish homotopical purity and blow-up theorems for finite abelian groups.Comment: Final version, to appear in Journal of Topology. arXiv admin note:
text overlap with arXiv:1403.191
Iterated wreath product of the simplex category and iterated loop spaces
Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of
-fold loop spaces is shown to be equivalent to the homotopy theory of
reduced -spaces, where is an iterated wreath product of
the simplex category . A sequence of functors from to
allows for an alternative description of the Segal-spectrum associated
to a -space. In particular, each Eilenberg-MacLane space has
a canonical reduced -set model
Higher quasi-categories vs higher Rezk spaces
We introduce a notion of n-quasi-categories as fibrant objects of a model
category structure on presheaves on Joyal's n-cell category \Theta_n. Our
definition comes from an idea of Cisinski and Joyal. However, we show that this
idea has to be slightly modified to get a reasonable notion. We construct two
Quillen equivalences between the model category of n-quasi-categories and the
model category of Rezk \Theta_n-spaces showing that n-quasi-categories are a
model for (\infty, n)-categories. For n = 1, we recover the two Quillen
equivalences defined by Joyal and Tierney between quasi-categories and complete
Segal spaces.Comment: 44 pages, v2: terminology changed (see Remark 5.27), Corollary 7.5
added, appendix A added, references added, v3: reorganization of Sections 5
and 6, more informal comments, new section characterizing strict n-categories
whose nerve is an n-quasi-category, numbering has change
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