Kerodon

Remark 4.3.3.32 (Associativity). Let $X$, $Y$, and $Z$ be simplicial sets. Then Remark 4.3.3.5 supplies a canonical isomorphism of simplicial sets $\alpha _{X,Y,Z}: X \star (Y \star Z) \simeq (X \star Y) \star Z$. These isomorphisms are associativity constraints for a monoidal structure on the category of simplicial sets, which is characterized (up to isomorphism) by the requirement that the equivalence $\operatorname{Fun}_{\ast }( \operatorname{Lin}^{\operatorname{op}}, \operatorname{Set}) \rightarrow \operatorname{Set_{\Delta }}$ of Proposition 4.3.3.11 can be promoted to a monoidal functor.