Divided power algebras and distributive laws

Games and General Distributive Laws in Boolean Algebras

The games G 1 (κ) and G η <λ(κ) are played by two players in η +complete and max(η+ , λ)-complete Boolean algebras, respectively. For cardinals η, κ such that κ<η = η or κ<η = κ, the (η, κ)-distributive law holds in a Boolean algebra B iff Player 1 does not have a winning strategy in G 1 (κ). Furthermore, for all cardinals κ, the (η,∞)-distributive law holds in B iff Player 1 does not have a wi...

Finiteness conditions and distributive laws for Boolean algebras

Klaus Ambos-Spies, Heidelberg Klaus Meer, Cottbus Marat M. Arslanov, Kazan Wolfram Pohlers, Münster Günter Asser, Greifswald Pavel Pudlak, Prague John T. Baldwin, Chicago Andrzej Rosłanowski, Omaha Douglas S. Bridges, Canterbury Jörg Rothe, Düsseldorf Ramon Jansana, Barcelona Wilfried Sieg, Pittsburgh Carl G. Jockusch, Urbana Stephen G. Simpson, State College, PA Alexander Kechris, Pasadena Mar...

Differential Equations in Divided Power Algebras

Operads, clones, and distributive laws

We show how non-symmetric operads (or multicategories), symmetric operads, and clones, arise from three suitable monads on Cat, each extending to a (pseudo-)monad on the bicategory of categories and profunctors. We also explain how other previous categorical analyses of operads (via Day’s tensor products, or via analytical functors) fit with the profunctor approach.

Cacti and filtered distributive laws

Motivated by the second author’s construction of a classifying space for the group of pure symmetric automorphisms of a free product, we introduce and study a family of topological operads, the operads of based cacti, defined for every pointed simplicial set .Y;p/ . These operads also admit linear versions, which are defined for every augmented graded cocommutative coalgebra C . We show that th...