Recall that we may define a functor $\xi:\Delta\to \operatorname{Poset}$ sending a simplex $[n]$ to the set of monotone injections $[k]\hookrightarrow [n]$ for $k\geq 0$ (effectively, $k\leq n$ as well, but this follows from injectivity) partially ordered by inclusion. Composing this with the obvious inclusion $\iota:\operatorname{Poset}\hookrightarrow \operatorname{Cat}$ and the nerve $\operatorname{sSet}\to \operatorname{sSet}$, this yields a functor $\Delta\to \operatorname{sSet}$, and by the universal property of presheaf categories, there exists a unique colimit-preserving lift $\operatorname{Sd}:\operatorname{sSet}\to \operatorname{sSet}$ By adjoint functor nonsense, we obtain an adjunction $$\operatorname{Sd}:\operatorname{sSet}\leftrightarrows \operatorname{sSet}:\operatorname{Ex}.$$

The functor $\operatorname{Sd}$, unsurprisingly is called the barycentric subdivision, since we obtain an isomorphism $$\operatorname{Sd}\circ N_{\mathcal{CS}}(-)\cong N_{\mathcal{CS}}\circ \xi_\mathcal{CS}(-)$$ of functors $\mathcal{CS}\to sSet$ where $\mathcal{CS}$ is the classical category of combinatorial simplicial complexes, $N_{CS}:\mathcal{CS}\to sSet$ is the nerve of simplicial complexes, and $\xi_{\mathcal{CS}}:\mathcal{CS}\to \mathcal{CS}$ is the classical barycentric subdivision of simplicial complexes.

Where does the two-letter abbreviation for $\operatorname{Ex}$ come from? Does it actually stand for an english word? Does it have a classical analogue for combinatorial or topological simplicial complexes?

(I wasn't sure if I should tag this as a soft-question, so I added some gratuitous background and a mathematical question to even things out. I have marked this question community wiki, however, since I would call for wikification if it were asked by somebody else).