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Bibliographic Details
Main Author: Plakhotnikov, Alexander
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.17623
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author Plakhotnikov, Alexander
author_facet Plakhotnikov, Alexander
contents In this note we attempt to propose a categorical framework for the Ricci flow, treating it as a sequence of functors connecting the stack of Riemannian metrics to the category of geometric decompositions via singular flow spacetimes. To rigorize the domain of the flow, we adapt the definition of differentiable stacks to the site of Banach manifolds. We demonstrate that the Ricci flow defines a stratification of this stack.
format Preprint
id arxiv_https___arxiv_org_abs_2601_17623
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Ricci flow as functor
Plakhotnikov, Alexander
Category Theory
In this note we attempt to propose a categorical framework for the Ricci flow, treating it as a sequence of functors connecting the stack of Riemannian metrics to the category of geometric decompositions via singular flow spacetimes. To rigorize the domain of the flow, we adapt the definition of differentiable stacks to the site of Banach manifolds. We demonstrate that the Ricci flow defines a stratification of this stack.
title Ricci flow as functor
topic Category Theory
url https://arxiv.org/abs/2601.17623