Mackey functors, induction from restriction functors and coinduction from transfer functors
نویسندگان
چکیده
منابع مشابه
Stratifications and Mackey Functors Ii: Globally Defined Mackey Functors
We describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite pa...
متن کاملFused Mackey functors
Let G be a finite group. In [5], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for G and biset functors defined on subgroups of G and bifree bisets as morphisms. This paper proposes a different approach to this problem, from the point of view of various categories of G-sets. In particular, the category G-set of fused G-sets is introduced, as well as th...
متن کاملMackey Functors and Bisets
For any finite group G, we define a bifunctor from the Dress category of finite G-sets to the conjugation biset category, whose objects are subgroups of G, and whose morphisms are generated by certain bifree bisets. Any additive functor from the conjugation biset category to abelian groups yields a Mackey functor by composition. We characterize the Mackey functors which arise in this way.
متن کاملResolutions of Mackey functors
I will build some standard resolutions for Mackey functors which are projective relative to p-subgroups. Those resolutions are closely related to the poset of p-subgroups. They lead to generalizations of known results on cohomology. They give a way to compute the Cartan matrix for Mackey functors, in terms of p-permutation modules, and to precise the structure of projective Mackey functors. The...
متن کاملA Remark on Mackey-functors
In the following note we characterize the category of Mackey-functors from a category ~, satisfying a few assumptions, to a category ~ as the category of functors from Sp(~), the category of "spans" in ~, to ~ which preserve finite products. This caracterization permits to apply all results on categories of functors preserving a given class of limits to the case of Mackey-functors. We recall (c...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.04.026