Geodesic
Contravariance through enrichment
Theory and applications of categories, Tome 33 (2018), pp. 95-130

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 18D20, 18D05
Keywords: opposite category, contravariant functor, generalized multicategory, enriched category, coherence theorem 
@article{TAC_2018_33_a4,
     author = {Michael Shulman},
     title = {Contravariance through enrichment},
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     pages = {95--130},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a4/}
}
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Michael Shulman. Contravariance through enrichment. Theory and applications of categories, Tome 33 (2018), pp. 95-130. http://geodesic.mathdoc.fr/item/TAC_2018_33_a4/