Polynomial functors and polynomial monads
By Nicola Gambino, Joachim Kock. Mathematical Proceedings of the Cambridge Philosophical Society, 2009
181 citations recorded by the source corpus.
Abstract We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a11ebe3ac0b94910cfa3422e077144192fc41f82
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Andrew Justin Blumberg
- M. Hill
- Nicola Gambino
- Mark Weber
- Christian Sattler
- Joachim Kock
- Clark Barwick
- L. Pereira
In Geometry and Topology
- Andrew Justin Blumberg
- M. Hill
- Nicola Gambino
- Mark Weber
- Christian Sattler
- Clark Barwick
- A. Mathew
- D. Gepner
In Mathematical Physics
- Andrew Justin Blumberg
- M. Hill
- Nicola Gambino
- Mark Weber
- Christian Sattler
- Joachim Kock
- Clark Barwick
- A. Mathew
Citations in the corpus
- The Frobenius condition, right properness, and uniform fibrations (2015, background): “Note that this is the polynomial endofunctor, in the sense of [14], associated to the diagram”
- Incomplete Tambara functors (2016, methodology): “For any wide, pullback stable subcategory D of SetG, a D-Tambara functor has an underlying Mackey functor.”
- Polynomials in categories with pullbacks (2011, background): “Composing these functors gives P(p) : Set/In → Set/Out the polynomial functor corresponding to the polynomial p. Functors of the form ∆p1 , Πp2 and Σp3 are part of the bread and butter of category theory.”