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...

One of the most exciting developments in representation theory in the recent years was the discovery of the Kazhdan-Lusztig functor [KL93a, KL93b, KL94a, KL94b], which is a tensor functor from the fusion category of representations of an affine Lie algebra to the category of representations of the corresponding quantum group, and is often an equivalence of categories. Informally speaking, this ...

We shall show that every stable equivalence (functor) between representation-finite selfinjective algebras not of type (D3m, s/3, 1) with m ≥ 2, 3 s lifts to a standard derived equivalence. This implies that all stable equivalences between these algebras are of Morita type.

For a fixed inverse semigroup S, there are two natural categories of left actions of S: the category Fact of unitary actions of S on sets X meaning actions where SX = X, and the category Étale of étale actions meaning those unitary actions equipped with a function p : X → E(S), to the set of idempotents of S, such that p(x)x = x and p(sx) = ses∗, where s∗ denotes the inverse of s. The category ...

We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence dg-categories between multiplets for supertranslation algebra equivariant modules over its Chevalley-Eilenberg cochains. This is closely linked to Koszul duality algebra. After introducing describing category supermultiplets, we define construction explicitly as dg-functor. th...

We extend the results of Drinfeld on the Drinfeld functor to the case l ≥ n. We present the character of finite-dimensional representations of the Yangian Y (sln) in terms of the Kazhdan-Lusztig polynomials as a consequence. Introduction In this article we study the representations of the Yangian Y (sln). The Yangian is a quantum group introduced by V. G. Drinfeld ([D1]). The parameterization o...

Given a category with a stable system of monics, one can form the corresponding category of partial maps. To each map in this category there is, on the domain of the map, an associated idempotent, which measures the degree of partiality. This structure is captured abstractly by the notion of a restriction category, in which every arrow is required to have such an associated idempotent. Categori...

Given a ring A and an A-coring C we study when the forgetful functor from the category of right C-comodules to the category of right A-modules and its right adjoint − ⊗A C are separable. We then proceed to study when the induction functor − ⊗A C is also the left adjoint of the forgetful functor. This question is closely related to the problem when A → AHom(C, A) is a Frobenius extension. We int...

We investigate the problem when tensor functor by a bimodule yields singular equivalence. It turns out that this is equivalent to one Hom given same induces triangle equivalence between homotopy categories of acyclic complexes injective modules. give conditions on appears in pair bimodules, defines with level. construct an explicit combinatorial manner, which quadratic monomial algebra and its ...