Geodesic
Iterated icons
Theory and applications of categories, Tome 29 (2014), pp. 929-977 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We study the totality of categories weakly enriched in a monoidal bicategory using a notion of enriched icon as 2-cells. We show that when the monoidal bicategory in question is symmetric then this process can be iterated. We show that starting from the symmetric monoidal bicategory Cat and performing the construction twice yields a convenient symmetric monoidal bicategory of partially strict tricategories. We show that restricting to the doubly degenerate ones immediately gives the correct bicategory of `2-tuply monoidal categories' missing from our earlier studies of the Periodic Table. We propose a generalisation to all $k$-tuply monoidal $n$-categories.

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Classification : Primary 18A05, 18D05, 18D10, 18D20
Keywords: symmetric monoidal bicategory, icon, enriched category 
@article{TAC_2014_29_a31,
     author = {Eugenia Cheng and Nick Gurski},
     title = {Iterated icons},
     journal = {Theory and applications of categories},
     pages = {929--977},
     year = {2014},
     volume = {29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a31/}
}
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Eugenia Cheng; Nick Gurski. Iterated icons. Theory and applications of categories, Tome 29 (2014), pp. 929-977. http://geodesic.mathdoc.fr/item/TAC_2014_29_a31/