Haugseng, RuneLinskens, SilNuiten, JoostHebestreit, Fabian2023-12-082023-12-082023-12-07Haugseng, R, Linskens, S, Nuiten, J & Hebestreit, F 2023, 'Two-variable fibrations, factorisation systems and categories of spans', Forum of Mathematics, Sigma, vol. 11, no. 2023, e111, pp. 1-70. https://doi.org/10.1017/fms.2023.1072050-5094https://hdl.handle.net/2164/22379Open Access via the CUP agreement Funding statement During the preparation of this text, FH and SL were members of the Hausdorff Center for Mathematics at the University of Bonn funded by the German Research Foundation (DFG), and FH was furthermore a member of the cluster ‘Mathematics Münster: Dynamics-Geometry-Structure’ at the University of Münster under grant nos. EXC 2047 and EXC 2044, respectively. FH would also like to thank the Mittag-Leffler Institute for its hospitality during the research program ‘Higher Algebraic Structures in Algebra, Topology and Geometry’, supported by the Swedish Research Council (VR) under grant no. 2016-06596. FH and JN were further supported by the European Research Council (ERC) through the grants ‘Moduli Spaces, Manifolds and Arithmetic’, grant no. 682922, and ‘Derived Symplectic Geometry and Applications’, grant no. 768679, respectively. SL was supported by the DFG Schwerpunktprogramm 1786 ‘Homotopy Theory and Algebraic Geometry’ (project ID SCHW 860/1-1).70672157engQA MathematicsEuropean Research Council682922QAJournal article10.1017/fms.2023.107112023