<p>Mathematics shapes our thinking around the socio-ecological, from analysing the rates of change of the climate to predicting the boundaries of a river over time. Such mathematics have become the norm, yet they are necessarily limited in the stories they can tell and the perspectives and worlds that they have to offer. Inspired by the work of Eugenia Cheng, we are interested in how category theory might offer us alternative ways of visualising and realising sustainable futures other than the normative approaches of abstraction and application which rely on assumptions of representability, objectivity and exteriority. We work with category theory’s shift of attention away from a priori objects and properties, in which sustainability would privilege the maintenance of a single future (oft envisioned for an undifferentiated notion of humanity), and instead focus on generating contextual relation/difference from within, following Indigenous scholarship that urges seeking attunement with local concerns. Through this relational focus, we find attention to the implicit axiological choices that we make when we model (and create) the world, and the ontological necessity of a mathematics that allows for multiple realities and futures. Our argument is not that we should all learn category theory; rather, we show how thinking categorically alerts us to how we might perturb and reimagine school mathematics in a way that requires our attention to contingency and attunement—including not just the human but the more-than-human as well, from bears to soil and waterways. This text is part of the article collection entitled “Mathematics Education for Sustainable Futures” (available at <a href="https://link.springer.com/collections/acebaagbha">https://link.springer.com/collections/acebaagbha</a>).</p>