Topological quantum many-body systems on the lattice are characterized by having the property that their low energy effective theories are TQFTs. Levin–Wen models are classes of spin systems on the 2D lattice whose low energy effective theories are Turaev–Viro TQFTs. The problem (from a mathematician's perspective) is that low energy effective theories are not at all well-defined! This leads to the question: for systems that (supposedly) exhibit topological order, how can we see the emergent TQFT directly on the lattice in the infinite volume limit? We will discuss our recently proposed approach to mathematically formalize the ideas of topological holography in terms of boundary algebras, and explain how this provides a solution for systems with local topological order.