Geodesic
Weak vertical composition II: totalities
Theory and applications of categories, Tome 41 (2024), pp. 995-1043

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We continue our study of semi-strict tricategories in which the only weakness is in vertical composition. We assemble the doubly-degenerate such tricategories into a 2-category, defining weak functors and transformations. We exhibit a biadjoint biequivalence between this 2-category and the 2-category of braided (weakly) monoidal categories, braided (weakly) monoidal functors, and monoidal transformations.

Publié le :
Classification : 18D05, 18D10, 18D20
Keywords: tricategory, degenerate, braided monoidal category, enrichment, icon 
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     author = {Eugenia Cheng and Alexander S. Corner},
     title = {Weak vertical composition {II:} totalities},
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     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a30/}
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Eugenia Cheng; Alexander S. Corner. Weak vertical composition II: totalities. Theory and applications of categories, Tome 41 (2024), pp. 995-1043. http://geodesic.mathdoc.fr/item/TAC_2024_41_a30/