We review the condensation completion of a modular tensor category $\mathcal{C}$, which yields a fusion 2-category $\mathrm{\Sigma }\mathcal{C}$ of separable algebras, bimodules over algebras, and bimodule maps in $\mathcal{C}$. Physically, $\mathrm{\Sigma }\mathcal{C}$ is the fusion 2-category of codimension-1 defects, codimension-2 defects and instantons in the $2+1\mathrm{D}$ topological order $\mathcal{C}$. We realize the rough-rough wall and $e\text{−}m$ exchange wall in the toric code model on the lattice by deforming the Hamiltonian based on the corresponding algebraic data. We apply condensation completion to the toric code, $3\mathbf{F}$, two-layer semion and ${\mathbb{Z}}_4$ topological orders, and explicitly enumerate their $1\mathrm{d}$ and $0\mathrm{d}$ defects along with fusion rules. We also mention other applications of condensation completion: alternative interpretations of condensation completion of a braided fusion category; condensation completion of the category of symmetry charges and its correspondence to gapped phases with symmetry; for a topological order $\mathcal{C}$, one can find all gapped boundaries of the stacking of $\mathcal{C}$ with its time-reversal conjugate through computing the condensation completion of $\mathcal{C}$.

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• Anyons
• Defects
• Topological phases of matter
• Abstract algebra