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arXiv · 2403.08087

Hochschild cohomology in toposes

Cameron Michie·Ivan Tomasic
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Abstract

We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute Hochschild cohomology. By specialising to the topos of difference sets, we obtain a theory of internal difference Hochschild cohomology, and compare it to the absolute Hochschild cohomology through the Grothendieck and hypercohomology spectral sequences. We provide a systematic and detailed treatment of tensor products in suitable toposes in hope to complete the existing literature.

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Cameron Michie, Ivan Tomasic. 2024-03-12. Hochschild cohomology in toposes. https://arxiv.org/abs/2403.08087

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