A rational Mackey functor M for a compact Lie group G can be viewed as a collection of sheaves on spaces of conjugacy classes of subgroups, one for each closed subgroup H, related by restriction maps only. This in turn may be speciied by giving a suitably continuous family consisting of a Q 0 (W G (H))-module V (H) for each closed subgroup H with restriction maps V (^ K) ?! V (K) whenever K is ...

sl 3-Foams and the Khovanov-Lauda categorification of quantum sl k. Abstract In this paper I define certain interesting 2-functors from the Khovanov-Lauda 2-category which categorifies quantum sl k , for any k > 1, to a 2-category of universal sl 3 foams with corners. For want of a better name I use the term foamation to indicate those 2-functors. I conjecture the existence of similar 2-functor...

Brown representability approximates the homotopy category of spectra by means of cohomology functors defined on finite spectra. We will show that if a model category K is suitably determined by λ-small objects then its homotopy category Ho(K) is approximated by cohomology functors defined on those λ-small objects. In the case of simplicial sets, we have λ = ω 1 , i.e., λ-small means countable.

Tannaka’s theorem states that a linear algebraic group G is determined by the category of finite-dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.

Brown representability approximates the homotopy category of spectra by means of cohomology functors defined on finite spectra. We will show that if a model category K is suitably determined by λ-small objects then its homotopy category Ho(K) is approximated by cohomology functors defined on those λ-small objects. In the case of simplicial sets, we have λ = ω1, i.e., λ-small means countable.

A. Introduction: There are several useful reviews on rare kaon decays and related topics [1–14]. Activity in rare kaon decays can be divided roughly into four categories: 1. Searches for explicit violations of the Standard Model 2. Measurements of Standard Model parameters 3. Searches for CP violation 4. Studies of strong interactions at low energy. The paradigm of Category 1 is the lepton flav...