In characteristic zero, Bezrukavnikov has shown that the category of perverse coherent sheaves on the nilpotent cone of a simply connected semisimple algebraic group is quasi-hereditary, and that it is derived-equivalent to the category of (ordinary) coherent sheaves. We prove that graded versions of these results also hold in good positive characteristic.

We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a Kc∘Vs on each -category K. also characterise Eilenberg-Moore algebras as weakly locally convex K-cones, its algebra morphisms continuous linear maps. In addition, we explicitly describe distributive law over Kc, which allows us to show any (resp., convex, linear) topological cone is K-cone. give an exam...

General definitions for causal structures on manifolds of dimension d + 1 > 2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or diffeomorphic abstraction from the standard null cone variety in IR. Weak () and strong () local cone (LC) structures refer to the cone itself or a manifold thick...

General definitions for causal structures on manifolds of dimension d + 1 > 2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or diffeomorphic abstraction from the standard null cone variety in IR d+1. Weak (C) and strong (C m) local cone (LC) structures refer to the cone itself or a manifo...

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.

We show that the mapping cone of a morphism of differential graded Lie algebras χ : L → M can be canonically endowed with an L∞-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L∞-algebras. The associated deformation functor coincides with the one introduced by t...