Polynomials in categories with pullbacks

By Mark Weber. Theory and Applications of Categories, 2011

54 citations recorded by the source corpus.

The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category E, is generalised for E just having pullbacks. The 2-categorical analogue of the theory of polynomials and polynomial functors is given, and its relationship with Street's theory of fibrations within 2-categories is explored. Johnstone's notion of "bagdomain data" is adapted to the present framework to make it easier to completely exhibit examples of polynomial monads.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e073681f979f3efa57f9f1ded49ee637db983ec4

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

1. Andrew Justin Blumberg
2. M. Hill
3. Joachim Kock
4. Nicola Gambino
5. Ben Webster
6. Bob Coecke
7. L. Pereira
8. P. Bonventre

In Geometry and Topology

1. Andrew Justin Blumberg
2. M. Hill
3. Nicola Gambino
4. Joachim Kock
5. Ben Webster
6. Bob Coecke
7. A. Mathew
8. D. Gepner

In Mathematical Physics

1. Andrew Justin Blumberg
2. M. Hill
3. Nicola Gambino
4. Joachim Kock
5. Ben Webster
6. A. Mathew
7. Bob Coecke
8. D. Gepner

Citations in the corpus

• Incomplete Tambara functors (2016, methodology): “For any wide, pullback stable subcategory D of SetG, a D-Tambara functor has an underlying Mackey functor.”
• Homotopy theory for algebras over polynomial monads (2013, unknown): “An extension to categories with pullbacks has been studied by Weber [64].”
• Polynomial functors and polynomial monads (2009, background): “Weber [63], who also gives a deeper analysis of distributivity.”