Coinduction functor in representation stability theory

Coinduction functor in representation stability theory

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.

Coinduction 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 ...

Antifounded Coinduction in Type Theory

Capretta, Vene and myself have previously [2] studied antifounded algebras as algebras supporting a form of coinduction in a category-theoretic setting, arising as the dual concept of wellfounded coalgebras. Wellfounded coalgebras are a category theorist’s take on coalgebras supporting induction, introduced by Taylor [4]. Informally, wellfoundedness of a coalgebra means that a subobject of its ...

Representation theory and homological stability

We introduce the idea of representation stability (and several variations) for a sequence of representations Vn of groups Gn. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Represent...

The Functor Category ∗ Categorical Methods in Representation Theory, Bristol, Sept. 2012