Polynomial functors
An instance of practice informing theory, polynomial functors arose from the study of algebraic data types and containers but have since been recognized as an important categorical concept in their own right. Polynomial functors categorify the polynomials familiar from elementary algebra.
Topos Institute hosted a Workshop on Polynomial Functors in 2021 and 2022 .
Literature
Books
- Spivak & Niu, 2023, draft: Polynomial functors: A general theory of interaction (GitHub )
Theory
- Kock, Joyal, Batanin, Mascari, 2010: Polynomial functors and opetopes (doi, arxiv)
- Kock, 2011: Polynomial functors and trees (doi, arxiv)
- Formalizes trees as polynomial functors subject to special conditions
- Kock, 2012: Data types with symmetries and polynomial functors over groupoids
(doi, arxiv)
- Connections with combinatorial species
- Gambino & Kock, 2013: Polynomial functors and polynomial monads (doi, arxiv)
- Myers & Spivak, 2020: Dirichlet functors are contravariant polynomial functors (arxiv)