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arXiv · 2603.19437

Signs in objective linear algebra, exemplified with exterior powers and determinants

Joachim Kock·Jesper Michael Møller
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Abstract

We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an objective treatment of exterior powers and determinants.

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Joachim Kock, Jesper Michael Møller. 2026-03-19. Signs in objective linear algebra, exemplified with exterior powers and determinants. https://arxiv.org/abs/2603.19437

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