The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transformation is a left exact functor. This functor and its first derived functor are evaluated on the global sections of a line bundle on the flag variety...

The preservation of weak pullbacks is studied for a functor M 1 on the category UMS of ultrametric spaces and nonexpansive mappings. The functor M 1 associates with an ultrametric space its collection of Borel probability measures with compact support. By application of the Max-ow Min-cut Theorem of graph theory a mediating morphism for a weak pullback diagram can be constructed in SET. It is s...

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 ...

We will show that Banach spaces are (a) monadic over complete metric via the unit ball functor and (b) pointed forgetful functor.

Gabriel showed that for a unital ring R, there exists bijective correspondence between the set of filters R and Giraud subcategories Mod(R). In this paper we prove result analogous to one given by Gabriel: small preadditive category C, left C Mod(C).

We prove that Morel-Voevodsky's stable $\mathbb{A}^1$-homotopy theory affords the universal coefficient system, giving rise to Grothendieck's six operations.

Essential to ML-style module systems is the concept of a functor, i.e. a function from modules to modules. Functors are ML’s way of providing generic data structures and reusable program components. Yet, there is a bewildering schism in ML land regarding the actual semantics of functors, familiar to experts under the code words generative vs. applicative. In Standard ML [3], each application of...

We provide a more economical refined version of Evrard’s categorical cocylinder factorization of a functor [Ev1,2]. We show that any functor between small categories can be factored into a homotopy equivalence followed by a (co)fibred functor which satisfies the (dual) assumption of Quillen’s Theorem B. Introduction The problem treated here is how to replace a functor f : C→ D between small cat...