Condensation Completion and Gapped Boundaries of 2+1D topological orders

For a 2+1D topological order, it's known that all the point-like defects in it form a modular tensor category (MTC) C. If we further consider codimension-1 and higher defects, they intuitively form a fusion 2-category, with (higher) morphisms as gapped domain walls. It turns out that such fusion 2-category is completely determined by the MTC C, by doing condensation completion. We denote the fusion 2-category as ∑C. A workable model for ∑C is the 2-category of separable algebras, algebra bimodules and bimodule maps in C. Also, by folding trick, every 1d gapped domain wall in C corresponds to a gapped boundary of the quantum double of C, which can be given by condensing a certain Lagrangian algebra in the quantum double of C. So there will be a correspondence between the separable algebras in C and Lagrangian algebras in its quantum double. We worked out the explicit condensation completion data for some topological orders, and computed the corresponding gapped boundary of their quantum double for each 1d gapped domain wall in the topological orders.