Etale algebras over finite Heyting algebras

Kuznetsov Evgeny

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arXiv · 2410.23442

Etale algebras over finite Heyting algebras

Kuznetsov Evgeny

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Abstract

In this paper, we investigate the concept of local homeomorphism in Esakia spaces. We introduce the notion of etale Heyting H-algebra and establish category-theoretic duality for etale Heyting H-algebra in the case of finite Heyting algebra H. Furthermore, we give an identity that axiomatizes the variety of etale Heyting H-algebras when H is finite. We also show that the category of Stone space-valued (co)presheaves over a finite Esakia space X is equivalent to the slice category of local homeomorphisms over X. The fact is used to show that, in comparison with the case of general Heyting H-algebras, it is easier to compute finite colimits in the category of etale Heyting H-algebras.

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BibTeX RIS

Kuznetsov Evgeny. 2024-10-30. Etale algebras over finite Heyting algebras. https://arxiv.org/abs/2410.23442

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