Interacting Hopf Algebras
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Abstract (arXiv)
We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IH is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R.
Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Mar 2014.
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Citing papers per year: 2021: 1; 2022: 0; 2023: 1; 2024: 2; 2025: 0; 2026: 1.
5 papers.
- 2021Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)cited by 4
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- 2026Complete Identification of Deep ReLU Networks through Lukasiewicz Logiccited by 1
- 2023Coinductive guide to inductive transformer headscited by 0
- 2026Complete Identification of Deep ReLU Networks through Lukasiewicz Logic30 Jan 2026
- 2024A Pattern Language for Machine Learning Tasks2 Jul 2024
- 2024On the Anatomy of Attention2 Jul 2024
- 2023Coinductive guide to inductive transformer heads3 Feb 2023
- 2021Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)22 Feb 2021