Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFaithfulness of a functor of Quillen
184
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
There exists a canonical functor from the category of fibrant objects of a model category modulo cylinder homotopy to its homotopy category. We show that this functor is faithful under certain conditions, but not in general.
rate research
Read More
In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.
We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological Andre-Quillen cohomology of the K(n)-local Spanier-Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable v_n-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computations to the algebraic geometry of isogenies between Lubin-Tate formal groups.
Let $mathcal{A}$ be a small abelian category. The purpose of this paper is to introduce and study a category $overline{mathcal{A}}$ which implicitly appears in construction of some TQFTs where $overline{mathcal{A}}$ is determined by $mathcal{A}$. If $mathcal{A}$ is the category of abelian groups, then the TQFTs obtained by Dijkgraaf-Witten theory of abelian groups or Turaev-Viro theory of bicommutative Hopf algebras factor through $overline{mathcal{A}}$ up to a scaling. In this paper, we go further by giving a sufficient condition for an $mathcal{A}$-valued Brown functor to extend to a homotopy-theoretic analogue of $overline{mathcal{A}}$-valued TQFT for arbitrary $mathcal{A}$. The results of this paper and our subsequent paper reproduces TQFTs obtained by DW theory and TV theory.
We prove a multiplicative version of the equivariant Barratt-Priddy-Quillen theorem, starting from the additive version proven in arXiv:1207.3459. The proof uses a multiplicative elaboration of an additive equivariant infinite loop space machine that manufactures orthogonal $G$-spectra from symmetric monoidal $G$-categories. The new machine produces highly structured associative ring and module $G$-spectra from appropriate multiplicative input. It relies on new operadic multicategories that are of considerable independent interest and are defined in a general, not necessarily equivariant or topological, context. Most of our work is focused on constructing and comparing them. We construct a multifunctor from the multicategory of symmetric monoidal $G$-categories to the multicategory of orthogonal $G$-spectra. With this machinery in place, we prove that the equivariant BPQ theorem can be lifted to a multiplicative equivalence. That is the heart of what is needed for the presheaf reconstruction of the category of $G$-spectra in arXiv:1110.3571.
Q-systems are unita
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
