New preprint on arXiv: In Topological and Geometric Perspectives on Homomorphism Indistinguishability (with Josse van Dobben de Bruyn, Jérémie Marquès, David E. Roberson, Gian Luca Spitzer, and Peter Zeman), we give an axiomatisation of homomorphism indistinguishability relations. We do so by observing that homomorphism indistinguishability relations correspond to ideals of a graph semiring algebra and applying Hilbert’s Nullstellensatz. This answers a question of Atserias, Kolaitis, and Wu (LICS 2021).