Polynomials as spans

2019/03/10 by Street, Ross · 1 citation
#18C15 #18D05 #18F20 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.03890

Abstract

The paper defines polynomials in a bicategory \mathscrM. Polynomials in bicategories Spn\mathscrC of spans in a finitely complete category \mathscrC agree with polynomials in \mathscrC as defined by Nicola Gambino and Joachim Kock, and by Mark Weber. When \mathscrM is calibrated, we obtain another bicategory Poly\mathscrM. We see that polynomials in \mathscrM have representations as pseudofunctors \mathscrM^op→ Cat. Calibrations are produced for the bicategory of relations in a regular category and for the bicategory of two-sided modules (distributors) between categories thereby providing new examples of bicategories of "polynomials".

Cited by

• Locally subcartesian closed categories

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