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  1. Article

    Coxeter groups, Coxeter monoids and the Bruhat order

    Associated with any Coxeter group is a Coxeter monoid, which has the same elements, and the same identity, but a different multiplication. (Some authors call these Coxeter monoids 0-Hecke monoids, because of t...

    Toby Kenney in Journal of Algebraic Combinatorics (2014)

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    Article

    Graphical algebras — a new approach to congruence lattices

    In 1970, H. Werner considered the question of which sublattices of partition lattices are congruence lattices for an algebra on the underlying set of the partition lattices. He showed that a complete sublattic...

    Toby Kenney in Algebra universalis (2010)

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    The General Theory of Diads

    A diad is a generalisation of a monad and a comonad. The idea is that we ignore the unit or counit, and consider only the natural transformations between T and T 2. It turns out that almos...

    Toby Kenney in Applied Categorical Structures (2010)

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    Diads and their Application to Topoi

    It is well known that the category of coalgebras for a finite-limit preserving comonad on a topos is again a topos, and the category of algebras for a finite-limit preserving monad is a topos if the monad is i...

    Toby Kenney in Applied Categorical Structures (2009)