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arXiv · 1606.05058

Contravariance through enrichment

Michael Shulman
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Abstract

We define strict and weak duality involutions on 2-categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2-category with a strict duality involution. For this purpose we introduce "2-categories with contravariance", a sort of enhanced 2-category with a basic notion of "contravariant morphism", which can be regarded either as generalized multicategories or as enriched categories. This enables a universal characterization of duality involutions using absolute weighted colimits, leading to a conceptual proof of the coherence theorem.

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Michael Shulman. 2016-06-16. Contravariance through enrichment. https://arxiv.org/abs/1606.05058

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