Polynomials as spans

The paper defines polynomials in a bicategory $\mathscr{M}$. Polynomials in bicategories $\mathrm{Spn}\mathscr{C} \$ of spans in a finitely complete category $\mathscr{C} \$ agree with polynomials in $\mathscr{C} \$ as defined by Nicola Gambino and Joachim Kock, and by Mark Weber. When $\mathscr{M}$ is \textit{calibrated}, we obtain another bicategory $\mathrm{Poly}\mathscr{M}$. We see that polynomials in $\mathscr{M}$ have representations as pseudofunctors $\mathscr{M}^{\mathrm{op}}\to \mathrm{Cat}$. 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".

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