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Joachim Kock

  1. Local fibered right adjoints are polynomial.

    Втр, 05/25/2010 - 15:01 — SomNambul
    Authors: Joachim Kock, Anders Kock
    Subjects: Category Theory
    Abstract

    For any locally cartesian closed category E, we prove that a local fibered
    right adjoint between slices of E is given by a polynomial. The slices in
    question are taken in a well known fibered sense.

  2. Polynomial functors and trees.

    Пт, 12/04/2009 - 16:01 — SomNambul
    Authors: Joachim Kock
    Subjects: Category Theory
    Abstract

    We explore the relationship between polynomial functors and (rooted) trees.
    In the first part we use polynomial functors to derive a new convenient
    formalism for trees, and obtain a natural and conceptual construction of the
    category $\Omega$ of Moerdijk and Weiss; its main properties are described in
    terms of some factorisation systems. Although the constructions are motivated
    and explained in terms of polynomial functors, they all amount to elementary
    manipulations with finite sets.

  3. Feynman graphs, and nerve theorem for compact symmetric multicategories (extended abstract).

    Чт, 08/20/2009 - 23:06 — SomNambul
    Authors: André Joyal, Joachim Kock
    Subjects: Quantum Algebra
    Abstract

    We describe a category of Feynman graphs and show how it relates to compact
    symmetric multicategories (coloured modular operads) just as linear orders
    relate to categories and rooted trees relate to multicategories. More
    specifically we obtain the following nerve theorem: compact symmetric
    multicategories can be characterised as presheaves on the category of Feynman
    graphs subject to a Segal condition. This text is a write-up of the
    second-named author's QPL6 talk; a more detailed account of this material will
    appear elsewhere.

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