Dilatations of categories, via their lean formalization

Arnaud Mayeux

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arXiv · 2608.09305

Dilatations of categories, via their lean formalization

Arnaud Mayeux

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Abstract

Given a category $\calC$ and a center, that is a collection of pairs $(d_i, N_i)$ consisting of a morphism $d_i$ and a sieve $N_i$ over its codomain, the dilatation of $\calC$ is a new category $\calC'$ in which every $n \in N_i$ factors, uniquely and functorially, through $d_i$. This paper presents the theory of dilatations of categories through a full formalization of the construction and its main theorems in the Lean~4 proof assistant, on top of the Mathlib library. An appendix collects a systematic dictionary between the mathematical statements and the Lean declarations that formalize them.

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Arnaud Mayeux. 2026-08-10. Dilatations of categories, via their lean formalization. https://arxiv.org/abs/2608.09305

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