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)
  • Gambino & Kock, 2013: Polynomial functors and polynomial monads (doi, arxiv)
    • Generalized in: Weber, 2015: Polynomials in categories with pullbacks (pdf, arxiv)
    • Introduced and motivated in: Clingman, 2019: Polynomial functors, a degree of generality (pdf)
  • Myers & Spivak, 2020: Dirichlet functors are contravariant polynomial functors (arxiv)