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arXiv · 1504.01408

The $p$-adic integers as final coalgebra

Prasit Bhattacharya
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Abstract

We express the classical $p$-adic integers $\hat{\mathbb{Z}_p}$, as a metric space, as a final colagebra to a certain endofunctor. We realize the addition and the multiplication on $\hat{\mathbb{Z}_p}$ as the coalgebra maps from $\hat{\mathbb{Z}_p} \times \hat{\mathbb{Z}_p}$.

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Prasit Bhattacharya. 2015-03-20. The $p$-adic integers as final coalgebra. https://arxiv.org/abs/1504.01408

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