  We provide a lattice regularization of all topological defects in minimal
models CFTs using RSOS and anyonic spin chains. For defects of type $(1,s)$, we
connect our result with the "topological symmetry" initially identified in
Fibonacci anyons [Phys. Rev. Lett. 98, 160409 (2007)], and the center of the
affine Temperley-Lieb algebra discussed in [1811.02551]. We show that the
topological nature of the defects is exact on the lattice as well. Our defects
of type $(r,1)$, in contrast, are only topological in the continuum limit.
Identifications are obtained by a mix of algebraic and Bethe-ansatz techniques.
Most of our discussion is framed in a Hamiltonian (or transfer matrix)
formalism, and direct and crossed channel are both discussed in detail. For
defects of type $(1,s)$, we also show how to implement their fusion, which
turns out to reproduce the tensor product of the underlying monoidal category
used to build the anyonic chain.
