Exploració per autor "Kock, Joachim"
Ara es mostren els items 1-13 de 13
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Decomposition spaces and restriction species
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (Oxford University Press, 2020-11)
Article
Accés obertWe show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general ... -
Decomposition spaces in combinatorics
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-12)
Report de recerca
Accés obertA decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new ... -
Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-07-31)
Article
Accés obertThis is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition ... -
Decomposition spaces, incidence algebras and Mobius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-08-20)
Article
Accés obertDecomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors (CULF) between decomposition spaces induce ... -
Decomposition spaces, incidence algebras and Möbius inversion
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2014-04-11)
Report de recerca
Accés obert -
Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-06-20)
Article
Accés obertThis is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality ... -
Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
Report de recerca
Accés obertThis is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality ... -
Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
Report de recerca
Accés obertThis is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space ... -
Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
Report de recerca
Accés obertDecomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra ... -
Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2014)
Article
Accés restringit per política de l'editorialWe prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. -
Groupoids and Faà di Bruno Formulae for green functions in bialgebras of trees
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Kock, Joachim (2012-07)
Report de recerca
Accés obertWe prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. For suitable choices ... -
Homotopy linear algebra
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-02)
Report de recerca
Accés obertBy homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ... -
Homotopy linear algebra
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-04)
Article
Accés obertBy homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...