This paper answers the following question: what algebraic structure on a category corresponds to an structure (in the sense of Stasheff) on the geometric realization of its nerve?
"Associahedra and weak monoidal structures on categories." Algebr. Geom. Topol. 12 (1) 469 - 492, 2012. https://doi.org/10.2140/agt.2012.12.469