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d-Representability of simplicial complexes of fixed dimension
Combinatorics d-Representability fixed dimension
2011/8/26
Abstract: Let K be a simplicial complex with vertex set V = {v_1,..., v_n}. The complex K is d-representable if there is a collection {C_1,...,C_n} of convex sets in R^d such that a subcollection {C_{...
Brown representability often fails for homotopy categories of complexes
Brown representability Adjoint functor Triangulated cate-gory
2011/2/22
We show that for the homotopy category K(Ab) of com-plexes of abelian groups, both Brown representability and Brown repre-sentability for the dual fail. We also provide an example of a localizing subc...
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, ...
Some Applications of the Lattice Finite Representability in Spaces of Measurable Functions
Integral operators Ultraproducts of spaces and maps
2010/3/1
We study the lattice finite representability of the Bochner space Lp(m1,Lq(m2)) in \ellp{\ellq}, 1 \le p,q < \infty, and then we characterize the ideal of the operators which factor through a lattice ...
Failure of Brown representability in derived categories
Brown representability derived categories
2010/10/29
Let T be a triangulated category with coproducts, C the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [Adams71]: All contravariant ...