Recent Submissions

  • Copower objects and their applications to finiteness in topoi 

    Kenney, Toby. 2006. "Copower objects and their applications to finiteness in topoi." Theory Appl.Categ. 16(32): 923-956.
    No abstract available.
  • Generating families in a topos 

    Kenney, Toby. 2006. "Generating families in a topos." Theory Appl.Categ. 16(31): 896-922.
    No abstract available.
  • Categories as monoids in Span, Rel and Sup 

    Kenney, Toby, and Robert Pare. 2011. "Categories as monoids in Span, Rel and Sup." Cah.Topol.G\'eom.Diff\'er.Cat\'eg. 52(3): 209-240.
    No abstract available.
  • Injective power objects and the axiom of choice 

    Kenney, Toby. 2011. "Injective power objects and the axiom of choice." Journal of Pure and Applied Algebra 215(2): 131-144.
    "The axiom of choice states that any set X of non-empty sets has a choice function-i.e. a function X -> f boolean OR X satisfying f (x) is an element of x for all x is an element of X. When we want to generalise this to a ...
  • The path relation for directed planar graphs in rectangles, and its relation to the free diad 

    Kenney, Toby. 2011. "The path relation for directed planar graphs in rectangles, and its relation to the free diad." Discrete Mathematics 311(6): 441-456.
    In this paper, we define the path relation of a directed graph to be the relation which relates two vertices if there is a path from the first to the second. We study the restriction of this relation to paths from sources ...
  • Diads and their Application to Topoi 

    Kenney, Toby. 2009. "Diads and their Application to Topoi." Applied Categorical Structures 17(6): 567-590.
    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 idempotent, ...
  • The General Theory of Diads 

    Kenney, Toby. 2010. "The General Theory of Diads." Applied Categorical Structures 18(5): 523-572.
    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 almost all the constructions that we ...
  • Graphical algebras - a new approach to congruence lattices 

    Kenney, Toby. 2010. "Graphical algebras - a new approach to congruence lattices." Algebra Universalis 64(3-4): 313-338.
    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 sublattice of a partition ...
  • Tensor Products of Sup-Lattices and Generalized Sup-Arrows 

    Kenney, T., and R. J. Wood. 2010. "Tensor Products of Sup-Lattices and Generalized Sup-Arrows." Theory and Applications of Categories 24: 266-287.
    An alternative description of the tensor product of sup-lattices is given with yet another description provided for the tensor product in the special case of CCD sup-lattices. In the course of developing the latter, ...
  • Hessian calculation for phylogenetic likelihood based on the pruning algorithm and its applications 

    Kenney, Toby, and Hong Gu. 2012. "Hessian calculation for phylogenetic likelihood based on the pruning algorithm and its applications." Stat.Appl.Genet.Mol.Biol. 11(4): 1444.
    No abstract available.
  • Partial generalized additive models: an information-theoretic approach for dealing with concurvity and selecting variables 

    Gu, Hong, Toby Kenney, and Mu Zhu. 2010. "Partial generalized additive models: an information-theoretic approach for dealing with concurvity and selecting variables." J.Comput.Graph.Statist. 19(3): 531-551.
    No abstract available.