Decomposition spaces are simplicial 88 -groupoids with an exactness property giving coherent associativity of its objective incidence (co)algebra. Our theory encompasses the Connes–Kreimer algebra, (derived) Hall algebras and Möbius inversion. This note describes joint work with J. Kock (Universitat Autònoma de Barcelona) and A. Tonks (Leicester)
Galvez, M. Decomposition Spaces and Incidence (Co)Algebras .. A: IRTATCA-Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra-CRM Programm. "Extended Abstracts Spring 2015 Interactions between Representation Theory, Algebraic Topology and Commutative Algebra". Barcelona, UB-IMUB: Birkhäuser Verlag, 2015, p. 69-74.