Browsing by Author "Kock, Joachim"

Decomposition spaces and restriction species
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (Oxford University Press, 20180912)
Article
Open AccessWe show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2Segal spaces), and that their associated coalgebras are an instance of the general ... 
Decomposition spaces, incidence algebras and Möbius inversion
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (20140411)
External research report
Open Access 
Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (20180620)
Article
Restricted access  publisher's policyThis 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 (201512)
External research report
Open AccessThis 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 (201512)
External research report
Open AccessThis 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 8groupoids. A decomposition space ... 
Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (20180731)
Article
Restricted access  publisher's policyThis 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 8groupoids. A decomposition ... 
Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (201512)
External research report
Open AccessDecomposition spaces are simplicial 8groupoids 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 ... 
Decomposition spaces, incidence algebras and Mobius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (20180820)
Article
Restricted access  publisher's policyDecomposition spaces are simplicial 8groupoids 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 in combinatorics
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (201612)
External research report
Open AccessA decomposition space (also called unital 2Segal 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 ... 
Groupoids and Faà di Bruno Formulae for green functions in bialgebras of trees
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Kock, Joachim (201207)
External research report
Open AccessWe prove a Faa di Bruno formula for the Green function in the bialgebra of Ptrees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. For suitable choices ... 
Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2014)
Article
Restricted access  publisher's policyWe prove a Faà di Bruno formula for the Green function in the bialgebra of Ptrees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. 
Homotopy linear algebra
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (201804)
Article
Open AccessBy homotopy linear algebra we mean the study of linear functors between slices of the 8category of 8groupoids, 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 (201602)
External research report
Open AccessBy homotopy linear algebra we mean the study of linear functors between slices of the 8category of 8groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...