Algebraic quantum field theory (AQFT) formalizes QFTs as functors assigning algebras (of observables) to spacetime regions, subject to physically motivated axioms such as causality. We present a colored operad that allows us to turn the AQFT axioms into structure by showing that the associated category of algebras is naturally isomorphic to the category of AQFTs. This approach induces a number of novel constructions for AQFTs and refines known ones (most notably Fredenhagen's universal algebra, which provides a local-to-global extension for AQFTs). Furthermore, it allows us to give a precise definition of homotopical AQFTs as algebras over a suitable resolution of the AQFT colored operad. Examples of homotopical AQFTs are obtained by computing homotopy invariants of ordinary AQFTs defined on spacetimes equipped with further structure (e.g. bundles with connection, spin structures, etc).

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