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It was well known that there are $e$-particles and $m$-strings in the3-dimensional (spatial dimension) toric code model, which realizes the3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result,however, shows that there are additional string-like topological defects in the3-dimensional $\mathbb{Z}_2$ topological order. In this work, we construct alltopological defects of codimension 2 and higher, and show that they form abraided fusion 2-category satisfying a braiding non-degeneracy condition.

Defects in the 3-dimensional toric code model form a braided fusion 2-category