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arXiv · 1501.00792

Building the bicategory Span$_2(\mathcal {C})$

Franciscus Rebro
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Abstract

Given any category $\mathcal{C}$ with pullbacks and a terminal object, we show that the data consisting of the objects of $\mathcal{C}$, the spans of $\mathcal{C}$, and the isomorphism classes of spans of spans of $\mathcal{C}$, forms a bicategory. We denote this bicategory Span$_2(\mathcal{C})$ and show that this construction can be applied to give a bicategory of $n$-manifolds, cobordisms of those manifolds, and cobordisms of cobordisms.

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Franciscus Rebro. 2015-01-05. Building the bicategory Span$_2(\mathcal {C})$. https://arxiv.org/abs/1501.00792

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