abstract: Many homological group properties are stable under taking amalgamated products and group extensions, and satisfy a more general combination theorem. Examples of such properties are homological finiteness properties, vanishing of L2-Betti numbers, vanishing of homology growth, the cheap rebuilding property, and many more. I will present an axiomatic proof of a combination theorem that applies to all properties above. Joint work with Clara Löh, Marco Moraschini, Roman Sauer, Matthias Uschold.