Dear all, Geoffrey Cruttwell will be coming to the University of Strathclyde, Glasgow, Scotland to give a 6 x 1 hour tutorial on tangent categories 13 to 16 October 2026, more precisely the following dates: Tuesday 13 October Wednesday 14 October Friday 16 October Neil Ghani will also give a 6 x 1 hour lecture series on containers/polynomial functors. The courses will take place in Livingstone Tower, which is part of the University of Strathclyde's campus in Glasgow City Centre. For more information, see    https://msp.cis.strath.ac.uk/tangentcats-2026/ . Attendance is free, but please register here for planning purposes: https://forms.cloud.microsoft/e/BFugK7iUqY . Registration deadline: Monday 5 October 2026. Best wishes, and hope to see you there, Fred # Abstracts ## Tangent categories tutorial (Geoffrey Cruttwell, Mount Allison University) Tangent categories are a "minimal" categorical setting for differential geometry. Previous work on categorical machine learning has used cartesian differential categories (and variants of it), but that abstraction is not flexible enough to work with learning on manifolds. Tangent categories enable one to "do differential geometry" on manifolds and many other settings, and thus represent the "next step" for the study of categorical machine learning. In this tutorial I'll introduce what tangent categories are, give a variety of models for their axioms, and show some of their theory. Basic category theory knowledge is assumed, but I will not assume any knowledge of differential geometry or categorical machine learning. ## Containers: Theory and Applications (Neil Ghani, Kodamai) A container is a strikingly simple idea: a set of prompts, and for each prompt a set of admissible responses. From this modest starting point comes an enormous range of structure — every ordinary data type arises as the least fixed point of a container, and the functors they denote, the polynomial functors, sit at the heart of type theory, category theory, and functional programming. A container is at once a data type and a typed interface, specifying for every prompt exactly which responses are valid, and it carries a rich algebra: several monoidal structures, a well-behaved notion of morphism, closed structure, and a derivative. This series introduces containers from the ground up, and then follows them into computer science. We cover the basic theory — the definition and its readings, the extension to polynomial functors, container morphisms, the monoidal and closed structures, free and cofree containers, monads over containers, and indexed and directed containers — before turning to applications: machine learning, agentic AI, theorem proving, and differential algebra.