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arXiv · 2610.38991

Grothendieck Pairs, Functors and Profinite Invariants

Daniel Echtler
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Abstract

As another variation of profinite properties, we define the notion of natural profinite invariants: functorial invariants, inducing isomorphisms for every Grothendieck pair. We give a characterisation of when adjoint functors are natural profinite invariants and describe a strategy on how to disprove natural profinite invariance. By means of examples we show that the notions of profinite invariance and natural profinite invariances are logically independent.

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Daniel Echtler. 2026-10-28. Grothendieck Pairs, Functors and Profinite Invariants. https://arxiv.org/abs/2610.38991

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