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Simple string diagrams and n-sesquicategories
Theory and applications of categories, Tome 38 (2022), pp. 1284-1325 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We define a monad T_n^D^* whose operations are encoded by simple string diagrams and we define n-sesquicategories as algebras over this monad. This monad encodes the compositional structure of n-dimensional string diagrams. We give a generators and relations description of T_n^D^*, which allows us to describe n-sesquicategories as globular sets equipped with associative and unital composition and whiskering operations. One can also see them as strict n-categories without interchange laws. Finally we give an inductive characterization of n-sesquicategories.

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Classification : 18N20, 18N30
Keywords: string diagrams, higher categories 
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     author = {Manuel Ara\'ujo},
     title = {Simple string diagrams and n-sesquicategories},
     journal = {Theory and applications of categories},
     pages = {1284--1325},
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     volume = {38},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a33/}
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Manuel Araújo. Simple string diagrams and n-sesquicategories. Theory and applications of categories, Tome 38 (2022), pp. 1284-1325. http://geodesic.mathdoc.fr/item/TAC_2022_38_a33/