We show that the stable module categories of certain selfinjective algebras of finite representation type having tree class An, Dn, E6, E7 or E8 are triangulated equivalent to ucluster categories of the corresponding Dynkin type. The proof relies on the “Morita” theorem for u-cluster categories by Keller and Reiten, along with the recent computation of Calabi-Yau dimensions of stable module cat...

We develop the homotopy theory of Euler characteristic (magnitude) of a category enriched in a monoidal model category. If a monoidal model category V is equipped with an Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler characteristic of V-enriched categories is also compatible with weak equivalences and fibrations in the canonical model structu...

To examine retrieval-induced forgetting (RIF) in schizophrenia, subjects studied category-exemplar words taken from either strong or weak categories, and then practiced retrieval by completing category word-stems on half of the word pairs. Patients had reduced recall and recognition, but showed the expected RIF effect of better recall of unpracticed items from unpracticed categories than for un...

In a previous paper we lifted Charles Rezk’s complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of “relative categories.” Here, we characterize simplicial localization functors among relative functors from relative categories to simplicial categories as any choice of homotopy inverse to the delocalization functor of Dwyer and the seco...

We introduce a self-dual, noncommutative, and noncocommutative Hopf algebra HGT which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the GrothendieckTeichmüller group for quasitensor categories. We also give a result which highly restricts the possibility for similar structures for higher weak n-categories (n ≥ 3) by showing that these structur...

Let V be a vertex operator algebra. It is shown that the categories of weak, admissible and ordinary g-twisted modules for the tensor product VOA V ⊗k are isomorphic to the categories of weak, admissible and ordinary V -modules respectively where g is a k cycle automorphism of V ⊗k. For arbitrary permutation automorphism g of V ⊗k the category of admissible g-twisted modules for V ⊗k is semi si...