Coinduction functor in representation stability theory
نویسندگان
چکیده
We study the coinduction functor on the category of FI-modules and its variants. Using the coinduction functor, we give new and simpler proofs of (generalizations of) various results on homological properties of FI-modules. We also prove that any finitely generated projective VI-module over a field of characteristic 0 is injective.
منابع مشابه
On Coinduction Functors between Categories of Comodules for Corings
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a more general coinduction functor between categories ...
متن کاملA Note On Coinduction Functors between Categories of Comodules for Corings
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a more general coinduction functor between categories ...
متن کاملCoinduction Functor and Simple Comodules *
Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (coinduction functor) which is right adjoint to the hom-functor represented by this comodule. Using the coinduction functor, we establish a bijective map between the set of representative classes of torsion simple right comodules and the set of representative classes of ...
متن کاملMonoidal Company for Accessible Functors
Distributive laws between functors are a fundamental tool in the theory of coalgebras. In the context of coinduction in complete lattices, they correspond to the so-called compatible functions, which enable enhancements of the coinductive proof technique. Amongst these, the greatest compatible function, called the companion, has recently been shown to satisfy many good properties. Categorically...
متن کاملLink homology and Frobenius extensions
We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant. AMS Subject Classification: 57M27 Frobenius systems. Suppose ι : R −→ A is an inclusion of commutative rings, and ι(1) = 1. The restriction functor Res : A−mod −→ R−mod has left and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. London Math. Society
دوره 92 شماره
صفحات -
تاریخ انتشار 2015