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K. Dosen

  1. Shuffles and Concatenations in Constructing of Graphs.

    Пт, 02/19/2010 - 16:01 — SomNambul
    Authors: K. Dosen, Z. Petric
    Subjects: Logic
    Abstract

    This is an investigation of the role of shuffling and concatenating in the
    theory of graph drawing. A simple syntactic description of these and related
    operations is proved complete in the context of finite partial orders, as
    general as possible. An explanation based on that is given for a previously
    investigated collapse of the permutohedron into the associahedron, and for
    collapses into other less familiar polyhedra, including the cyclohedron.

  2. Coherence for Monoidal Endofunctors.

    Пнд, 01/11/2010 - 16:01 — SomNambul
    Authors: K. Dosen, Z. Petric
    Subjects: Category Theory
    Abstract

    The goal of this paper is to prove coherence results with respect to
    relational graphs for monoidal endofunctors, i.e. endofunctors of a monoidal
    category that preserve the monoidal structure up to a natural transformation
    that need not be an isomorphism. These results are proved first in the absence
    of symmetry in the monoidal structure, and then with this symmetry.

  3. Coherence for Monoidal Monads and Comonads.

    Пнд, 01/11/2010 - 16:01 — SomNambul
    Authors: K. Dosen, Z. Petric
    Subjects: Category Theory
    Abstract

    The goal of this paper is to prove coherence results with respect to
    relational graphs for monoidal monads and comonads, i.e. monads and comonads in
    a monoidal category such that the endofunctor of the monad or comonad is a
    monoidal functor (this means that it preserves the monoidal structure up to a
    natural transformation that need not be an isomorphism). These results are
    proved first in the absence of symmetry in the monoidal structure, and then
    with this symmetry. The monoidal structure is also allowed to be given with
    finite products or finite coproducts.

  4. Isomorphic Formulae in Classical Propositional Logic.

    Втр, 12/08/2009 - 16:01 — SomNambul
    Authors: K. Dosen, Z. Petric
    Subjects: Logic
    Abstract

    Isomorphism between formulae is defined with respect to categories
    formalizing equality of deductions in classical propositional logic and in the
    multiplicative fragment of classical linear propositional logic caught by proof
    nets. This equality is motivated by generality of deductions. Characterizations
    are given for pairs of isomorphic formulae, which lead to decision procedures
    for this isomorphism.

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