The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a Morita context comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Mor...

Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of co...

Consider a fibration sequence F → E → B of topological spaces which is preserved as such by some functor L, so that LF → LE → LB is again a fibration sequence. Pull the fibration back along an arbitrary map X → B into the base space. Does the pullback fibration enjoy the same property? For most functors this is not to be expected, and we concentrate mostly on homotopical localization functors. ...

We construct a family of functors assigning an R-module to a flag of R-modules, where R is a commutative ring. As particular instances, we get flagged Schur functors and Schubert functors, the latter family being indexed by permutations. We identify Schubert functors for vexillary permutations with some flagged Schur functors, thus establishing a functorial analogue of a theorem from [6] and [1...

Let A be a commutative noetherian ring. We investigate a class of functors from ≪commutative A-algebras≫ to ≪sets≫, which we call coherent. When such a functor F in fact takes its values in ≪abelian groups≫, we show that there are only finitely many prime numbers p such that pF (A) is infinite, and that none of these primes are invertible in A. This (and related statements) yield information ab...

For a metric μ on finite set T, the minimum 0-extension problem 0-Ext[μ] is defined as follows: Given V⊇T and c:V2→Q+, minimize ∑c(xy)μ(γ(x),γ(y)) subject to γ:V→T,γ(t)=t(∀t∈T), where sum taken over all unordered pairs in V. This generalizes several classical combinatorial optimization problems such cut or multiterminal problem. Karzanov Hirai established complete classification of metrics for ...

Abstract. We calculate Ext• SL2(k) (∆(λ),∆(μ)), Ext• SL2(k) (L(λ),∆(μ)), Ext• SL2(k) (∆(λ), L(μ)), and Ext•SL2(k) (L(λ), L(μ)), where ∆(λ) is the Weyl module of highest weight λ, L(λ) is the simple SL2(k)-module of highest weight λ and our field k is algebraically closed of positive characteristic. We also get analogous results for the Dipper-Donkin quantisation. To do thus we construct the Lyn...