4 papers
Groupoid G-spans and matrices over group rings
Joachim Kock, Jesper M. Møller
When G is a finite abelian group, we define G-spans of groupoids and their associated matrices with entries in the group ring QG and show that composition of spans corresponds to m…
Signs in objective linear algebra, exemplified with exterior powers and determinants
Joachim Kock, Jesper Michael Møller
We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations.…
Abacus bicomodule configurations and the Bergner-Osorno-Ozornova-Rovelli-Scheimbauer equivalence
Joachim Kock, Thomas Jan Mikhail
A theorem of Bergner, Osorno, Ozornova, Rovelli, and Scheimbauer states an equivalence between 2-Segal spaces and certain augmented stable double Segal spaces. In this paper we est…
Free loop spaces and the Cauchy--Frobenius Lemma
Joachim Kock, Thomas Jan Mikhail
We upgrade the Cauchy--Frobenius Lemma (`Burnside's Lemma') to a homotopy equivalence of -groupoids, essentially given by double counting/Fubini in the free loop space of t…