### A band generated by two semilattices is regular.

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We prove that an Artin-Tits group of type $\tilde{C}$ is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the “generated group” method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type $\tilde{C}$, and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...