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The orthogonal subcategory problem in homotopy theory
Carles Casacuberta, Boris Chorny
It is known that the existence of localization with respect to an arbitrary (possibly proper) class of maps in the category of simplicial sets is implied by a large-cardinal axiom…
A generalization of Quillen's small object argument
Boris Chorny
We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessi…
Localization with respect to a class of maps II - Equivariant cellularization and its application
Boris Chorny
We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The te…
Localization with respect to a class of maps I - Equivariant localization of diagrams of spaces
Boris Chorny
Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand th…
Equivariant cellular homology and its applications
Boris Chorny
In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.