Segal’s student Leitch used a similar construction to describe a homotopy commutative cube (actually a *homotopy coherent cube*), cf. [@leitch], and this was used by Segal in his famous paper, [@segal], under the name of the ‘explosion’ of $\mathbb{A}$. All this was still in the topological framework and the link with the comonad resolution was still not in evidence. Although it seems likely that Kan knew of this link between homotopy coherence and the comonadic resolutions by at least 1980, (cf. ), the construction does not seem to appear in his work with Dwyer as being linked with coherence until much later. Cordier made the link explicit in [@cordier82] and showed how Leitch and Segal’s work fitted in to the pattern. His motivation was for the description of homotopy coherent diagrams of topological spaces. Other variants were also apparent in the early work of May on operads, and linked in with Stasheff’s work on higher associativity and commutativity ‘up to homotopy’.

Cordier and Porter, [@cordierporter86], used an analysis of a locally Kan simplicially enriched category involving this construction to prove a generalisation of Vogt’s theorem on categories of homotopy coherent diagrams of a given type. (We will return to this 