  Many monoidal-type objects are known to be classified by maps from the
Catalan simplicial set $\mathbb{C}$ to various nerves of categories and higher
categories. There are, for example, three different nerves of the 2-category of
categories $\mathsf{Cat}$ with the property that maps from $\mathbb{C}$ into
them are in one to one correspondence with strict monoidal, monoidal, and skew
monoidal categories. In this last case, the classification result can be
understood as justifying the definition of skew monoidal categories
intrinsically in terms of the structure of $\mathbb{C}$.
  In this paper, we consider a single nerve -- the homotopy coherent nerve of
$\mathsf{Cat}$ viewed as a one object simplicially enriched category -- and
verify that maps from $\mathbb{C}$ to it classify the three monoidal-type
categories mentioned above, as well as lax monoidal categories and
$\Sigma$-monoidal categories. Furthermore, we identify a new monoidal-type
category corresponding to the most general such maps and present them in the
usual way: a collection of data subject to explicit coherence requirements.
These results suggest that the space of maps from $\mathbb{C}$ to the coherent
nerve of $\mathsf{Cat}$ provides a uniform framework for the definition and
study of many species of monoidal-type category, old or new.
