Change Actions: Models of Generalised Differentiation — Mario Alvarez-Picallo & C. -H. Luke Ong (2019; FoSSaCS 2019). arXiv:1902.05465 (v3, PDF).
Develops the category theory of change actions: categories of change actions and differential maps, internal change actions in a cartesian category, and change action models as coalgebras of a copointed endofunctor, with tangent bundle functors. Shows that generalised cartesian differential categories give change action models, as do polynomials over Kleene algebras — whose derivatives are not additive, so change actions strictly generalise differential categories.
Sources: the paper, arXiv:1902.05465v3, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 2.2, Lemma 2.3: derivative condition; chain rule
- Definitions 2.5, 2.9: regular derivatives; the category
- Definition 2.13, Lemma 2.14: monoidal change actions; adjunction with the forgetful functor
- Theorems 3.1–3.2: products and terminal object in
- Definitions 4.1–4.2: change action model; tangent bundle functor
- Theorem 4.8: tangent bundles and exponentials
- Theorem 5.1: GCDCs give change action models