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Published online by Cambridge University Press: 27 September 2025
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- Polynomial FunctorsA Mathematical Theory of Interaction, pp. 453 - 460Publisher: Cambridge University PressPrint publication year: 2025
References
Abbott, Michael, Altenkirch, Thorsten, and Ghani, Neil. “Containers: Constructing strictly positive types”. In: Theoretical Computer Science 342.1 (2005). Applied Semantics: Selected Topics, pp. 3–27 (cit. on p. 46).Google Scholar
Abbott, Michael, Altenkirch, Thorsten, Ghani, Neil, and McBride, Conor. “Derivatives of containers”. In: International Conference on Typed Lambda Calculi and Applications. Springer. 2003, pp. 16–30 (cit. on p. 64).Google Scholar
Abbott, Michael Gordon. “Categories of Containers”. PhD thesis. University of Leicester, Aug. 2003 (cit. on p. 46).Google Scholar
Abou-Saleh, Faris, Cheney, James, Gibbons, Jeremy, McKinna, James, and Stevens, Perdita. “Reflections on monadic lenses”. In: A List of Successes That Can Change the World. Springer, 2016, pp. 1–31 (cit. on p. 91).Google Scholar
Aguiar, Marcelo. Internal Categories and Quantum Groups. Cornell University, 1997 (cit. on pp. 341, 361).Google Scholar
Altenkirch, Thorsten, Levy, Paul, and Staton, Sam. “Higher- Order Containers”. In: Springer Nature, June 2010, pp. 11–20 (cit. on p. 218).Google Scholar
Ahman, Danel and Uustalu, Tarmo. “Directed Containers as Categories”. In: EPTCS 207, 2016, pp. 89-98 (2016). eprint: arXiv:1604.01187 (cit. on pp. xviii, 361).Google Scholar
Batanin, Michael and De Leger, Florian. Polynomial monads and delooping of mapping spaces. 2020. eprint: arXiv: 1712.00904 (cit. on p. xvii).Google Scholar
Borceux, Francis. Handbook of categorical algebra 1. Vol. 50. Encyclopedia of Mathematics and Its Applications. Basic category theory. Cambridge University Press, 1994 (cit. on p. 22).Google Scholar
Beurier, Erwan, Pastor, Dominique, and Spivak, David I. “Memoryless systems generate the class of all discrete systems”. In: International Journal of Mathematics and Mathematical Sciences 2019 (2019) (cit. on p. 166).Google Scholar
Bohannon, Aaron, Pierce, Benjamin C, and Vaughan, Jeffrey A. “Relational lenses: A language for updatable views”. In: Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems. ACM. 2006, pp. 338–347 (cit. on p. 91).10.1145/1142351.1142399CrossRefGoogle Scholar
Capucci, Matteo. Diegetic representation of feedback in open games. 2022. eprint: arXiv:2206.12338 (cit. on p. 219).Google Scholar
Cheng, Eugenia. The Joy of Abstraction: An Exploration of Math, Category Theory, and Life. Cambridge University Press, 2022 (cit. on p. 22).Google Scholar
Carboni, Aurelio and Johnstone, Peter. “Connected limits, familial representability and Artin glueing”. In: Mathematical Structures in Computer Science 5.4 (1995), pp. 441–459 (cit. on p. 45).Google Scholar
Conway, John Horton. Regular algebra and finite machines. Courier Corporation, 2012 (cit. on p. 166).Google Scholar
Dwyer, W. G.. “Twisted Homological Stability for General Linear Groups”. In: Annals of Mathematics 111.2 (1980), pp. 239–251. issn:0003486X. url: http://www.jstor.org/stable/1971200 (cit. on p. 46).Google Scholar
Eilenberg, Samuel and MacLane, Saunders. “On the Groups H (П, n), II: Methods of Computation”. In: Annals of Mathematics 60.1 (1954), pp. 49–139. issn: 0003486X, 19398980. url: http://www.jstor.org/stable/1969702 (cit. on p. 46).Google Scholar
Fong, Brendan and Spivak, David I.. Seven Sketches in Compositionality: An Invitation to Applied Category Theory. Cambridge University Press, 2019 (cit. on p. 22).10.1017/9781108668804CrossRefGoogle Scholar
Garner, Richard. Polynomial comonads and comodules. Homotopy Type Theory Electronic Seminar Talks. 2019. url: https://www.youtube.com/watch?v=tW6HYnqn6eI (cit.on pp.xviii, 440).Google Scholar
Gambino, Nicola and Hyland, Martin. “Wellfounded trees and dependent polynomial functors”. In: International Workshop on Types for Proofs and Programs. Springer. 2003, pp. 210–225 (cit. on p. 45).Google Scholar
Garner, Richard and Hirschowitz, Tom. “Shapely monads and analytic functors”. In: Journal of Logic and Computation 28.1 (2018), pp. 33–83 (cit. on p. 440).10.1093/logcom/exx029CrossRefGoogle Scholar
Girard, Jean-Yves. “Normal functors, power series and λ-calculus”. In: Annals of Pure and Applied Logic 37.2 (1988), pp. 129–177. issn: 0168-0072 (cit. on p. 45).Google Scholar
Gibbons, Jeremy and Johnson, Michael. “Relating algebraic and coalgebraic descriptions of lenses”. In: Electronic Communications of the EASST 49 (2012) (cit. on p. 91).Google Scholar
Gambino, Nicola and Kock, Joachim. “Polynomial functors and polynomial monads”. In: Mathematical Proceedings of the Cambridge Philosophical Society 154.1 (Sept. 2012), pp. 153–192 (cit. on pp. 46, 273, 281).10.1017/S0305004112000394CrossRefGoogle Scholar
Goodwillie, T. “The differential calculus of homotopy functors”. In: Proceedings of the International Congress of Mathematicians. Vol. 1. 1990, pp. 621–630 (cit. on p. 46).Google Scholar
Hedges, Jules, Shprits, Evguenia, Winschel, Viktor, and Zahn, Philipp. Compositionality and string diagrams for game theory. 2016. eprint: arXiv:1604.06061 (cit. on p. 91).Google Scholar
Hedges, Jules. Coherence for lenses and open games. 2017. eprint: arXiv:1704.02230 (cit. on p. 91).Google Scholar
Hedges, Jules. Limits of bimorphic lenses. 2018. eprint: arXiv: 1808.05545 (cit. on pp. 71, 91).Google Scholar
Hedges, Jules. “Morphisms of open games”. In: Electronic Notes in Theoretical Computer Science 341 (2018), pp. 151–177 (cit. on p. 91).Google Scholar
Hancock, Peter and Setzer, Anton. “Interactive programs in dependent type theory”. In: Computer Science Logic: 14th International Workshop, CSL 2000 Annual Conference of the EACSL Proceedings 14. Springer. 2000, pp. 317–331 (cit. on p. xvi).Google Scholar
Hyvernat, Pierre. Interaction systems and linear Logic, a different games semantics. 2009. eprint: arXiv : 0905.4062 (cit. on p. 165).Google Scholar
Jacobs, Bart. Introduction to Coalgebra. Vol. 59. Cambridge University Press, 2017 (cit. on pp. 45, 271).Google Scholar
Joyal, André. “Une théorie combinatoire des séries formelles”. In: Advances in Mathematics 42.1 (1981), pp. 1–82 (cit. on p. 46).Google Scholar
Johnson, Michael, Rosebrugh, Robert, and Wood, Richard J. “Lenses, fibrations and universal translations”. In: Mathematical Structures in Computer Science 22.1 (2012), pp. 25–42 (cit. on p. 91).10.1017/S0960129511000442CrossRefGoogle Scholar
Kelly, G Max. “Doctrinal adjunction”. In: Category Seminar. Springer. 1974, pp. 257–280 (cit. on p. 426).Google Scholar
Kock, Joachim. “Notes on Polynomial Functors”. https://mat.uab.cat/~kock/cat/polynomial.pdf. Accessed 2023/12/04 (cit. on p. 46).Google Scholar
Leinster, Tom. Basic Category Theory. Vol. 143. Cambridge University Press, 2014 (cit. on p. 22).10.1017/CBO9781107360068CrossRefGoogle Scholar
Lurie, Jacob. (Infinity,2)-Categories and the Goodwillie Calculus I. 2009. arXiv: 0905.0462 [math.CT]. url: https://arxiv.org/abs/0905.0462 (cit. on p. 46).Google Scholar
Manes, Ernest G and Arbib, Michael A. Algebraic Approaches to Program Semantics. Springer Science & Business Media, 2012 (cit. on p. 45).Google Scholar
Macdonald, Ian G. “Polynomial functors and wreath products”. In: Journal of Pure and Applied Algebra 18.2 (1980), pp. 173–204 (cit. on p. 46).10.1016/0022-4049(80)90128-0CrossRefGoogle Scholar
Lane, Saunders Mac. Categories for the Working Mathematician. 2nd ed. Graduate Texts in Mathematics 5. Springer-Verlag, 1998 (cit. on p. 22).Google Scholar
McBride, Conor. “The derivative of a regular type is its type of one-hole contexts”. In: Unpublished Manuscript (2001), pp. 74–88 (cit. on p. 64).Google Scholar
McBride, Conor. “Let’s see how things unfold: Reconciling the infinite with the intensional”. In: International Conference on Algebra and Coalgebra in Computer Science. Springer. 2009, pp.113–126.Google Scholar
MacLane, Saunders and Moerdijk, leke. Sheaves in Geometry and Logic: A First Introduction to Topos Theory. Springer, 1992 (cit. on p. 19).Google Scholar
Moerdijk, leke and Palmgren, Erik. “Wellfounded trees in categories”. In: Annals of Pure and Applied Logic 104.1-3 (2000), pp. 189–218 (cit. on p. 45).Google Scholar
Contributors To nLab. Created limit — nLab. 2018. url: https://ncatlab.org/nlab/show/created+limit (cit. on p. 423).Google Scholar
Contributors To nLab. Connected limit — nLab. 2019. url: https://ncatlab.org/nlab/show/connected+limit (cit. on p. 276).Google Scholar
Contributors To nLab. lens (in computer science). http://ncatlab.org/nlab/show/lens%20%28in%20computer%20science%29. Revision 26. Aug. 2022 (cit. on p. 361).Google Scholar
Niu, Nelson and Spivak, David I.. Collectives: Compositional protocols for contributions and returns. 2022. arXiv:2112.11518 (cit. on p. 88).Google Scholar
O’Connor, Russell. Functor is to lens as applicative is to biplate: Introducing multiplate. 2011. eprint: arXiv: 1103.2841 (cit. on p. 91).Google Scholar
Paré, Robert. “Absolute coequalizers”. In: Category Theory, Homology Theory and Their Applications I. Ed. by Hilton, Peter J.. Springer, 1969, pp. 132–145 (cit. on p. 423).Google Scholar
Pierce, Benjamin C.. Basic Category Theory for Computer Scientists. MIT Press, 1991 (cit. on p. 22).10.7551/mitpress/1524.001.0001CrossRefGoogle Scholar
Porst, Hans-E. “Colimits of monoids”. In: Theory and Applications of Categories 34.17 (2019), pp. 456–467 (cit. on pp. 423, 425).Google Scholar
Riehl, Emily. Category Theory in Context. Courier Dover Publications, 2017 (cit. on pp. 11, 22).Google Scholar
Schur, Issai. “Über die rationalen Darstellungen der allgemeinen linearen Gruppe”. In: Ges. Abhandlungen 3 (1927), pp. 68–85 (cit. on p. 46).Google Scholar
Spivak, David I, Garner, Richard, and Fairbanks, Aaron David. “Functorial aggregation”. In: Journal of Pure and Applied Algebra (2025), p. 107883 (cit. on p. xvi).10.1016/j.jpaa.2025.107883CrossRefGoogle Scholar
Shapiro, Brandon. Familial Monads as Higher Category Theories. 2021. eprint: arXiv:2111.14796 (cit. on p. 440).Google Scholar
Shulman, Michael. “Framed bicategories and monoidal fibrations”. In: Theory and Applications of Categories 20 (2008), Paper No. 18, 650–738 (cit. on pp. 209, 213).Google Scholar
Spivak, David I.. “Functorial data migration”. In: Information and Computation 217 (2012), pp. 31–51 (cit. on p. 357).CrossRefGoogle Scholar
Spivak, David I.. Generalized Lens Categories via functors Cop → Cat. 2019. eprint: arXiv:1908.02202 (cit. on p. 91).Google Scholar
Spivak, David I.. Polynomial functors and Shannon entropy. 2022. eprint: arXiv:2201.12878 (cit. on p. 219).Google Scholar
Spivak, David I and Tan, Joshua. “Nesting of dynamical systems and mode-dependent networks”. In: Journal of Complex Networks 5.3 (2017), pp. 389–408 (cit. on p. 166).Google Scholar
Spivak, David I. and Wisnesky, Ryan. “Relational Foundations for Functorial Data Migration”. In: Proceedings of the 15th Symposium on Database Programming Languages. DBPL. Pittsburgh, PA: ACM, 2015, pp. 21–28 (cit. on p. 436).10.1145/2815072.2815075CrossRefGoogle Scholar
Weber, Mark. “Familial 2-Functors and Parametric Right Adjoints”. In: Theory and Applications of Categories 18 (2007), Paper No. 22, 665–732 (cit. on p. 440).Google Scholar
Contributors To Wikipedia. Polynomial functor — Wikipedia, The Free Encyclopedia. [Online; accessed 03-April-2025]. 2024. url:%5Curl%7Bhttps://en.wikipedia.org/wiki/Polynomial_functor%7D (cit. on p. 46).Google Scholar
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