  The Tamari order is a central object in algebraic combinatorics and many
other areas. Defined as the transitive closure of an associativity law, the
Tamari order possesses a surprisingly rich structure: it is a
congruence-uniform lattice. We consider a larger class of posets, the
Grid-Tamari orders, which arise as an ordering on the facets of the non-kissing
complex introduced by Pylyavskyy, Petersen, and Speyer. In addition to Tamari
orders, some interesting examples of Grid-Tamari orders include the Type A
Cambrian lattices and Grassmann-Tamari orders. We prove that the Grid-Tamari
orders are congruence-uniform lattices, which resolves a conjecture of Santos,
Stump, and Welker. Towards this goal, we define a closure operator on sets of
paths in a square grid, and prove that the biclosed sets of paths, ordered by
inclusion, form a congruence-uniform lattice. We then prove that the
Grid-Tamari order is a quotient lattice of the corresponding lattice of
biclosed sets.
