The Verity-Gray tensor product or lax Gray tensor product of stratified simplicial sets is a tensor product on the category of stratified simplicial sets which when restricted to complicial sets, i.e. omega-nerves of strict omega-categories reproduces the Crans-Gray tensor product on strict -categories.
Let and be stratified simplicial sets. Then their Verity-Gray tensor product is given by
where is the cartesian product of simplicial sets (hence the standard monoidal structure on SSet), while , the set of thin cells, is for the Gray product, and for the lax-Gray product it is enlarged as described in the paper.
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