A note on fixed points of endofunctors

Aleksandr Luzhenkov

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arXiv · 1704.04414

A note on fixed points of endofunctors

Aleksandr Luzhenkov

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Abstract

In this note, we deal with the fixed points of an endofunctor $F: \mathcal{C} \longrightarrow \mathcal{C}$. Three classes of fixed points are introduced, and the case when $F$ is an endomorphism of a category with pretopology is investigated. We show existence of induced structures on the category of fixed points, and, when a pretopology is defined, give a characterization of fixed points in terms of sheaf cohomology on $\mathcal{C}$.

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Aleksandr Luzhenkov. 2017-04-14. A note on fixed points of endofunctors. https://arxiv.org/abs/1704.04414

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