A Clifford Theory for Grade Coalgebras: Applications

Clifford Theory for Cocentral Extensions

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is cocentral.

Clifford Theory for Association Schemes

Clifford theory of finite groups is generalized to association schemes. It shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme. The restriction of an irreducible character of a scheme to a strongly normal closed subset coniatns conjugate characters with same multiplicities. Moreover some strong relations are obtained.

Clifford theory for tensor categories

A graded tensor category over a group G will be called a strongly G-graded tensor category if every homogeneous component has at least one invertible object. Our main result is a description of the module categories over a strongly G-graded tensor category as induced from module categories over tensor subcategories associated with the subgroups of G.

Lie Coalgebras and Rational Homotopy Theory, I: Graph Coalgebras

A modal proof theory for final polynomial coalgebras

An infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets. The canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor. The states of this final coalgebra are certain “maximal” sets of formulas that have natural syntactic closure properties. The syntax of these logics e...