  We generalize the operadic approach to algebraic quantum field theory
[arXiv:1709.08657] to a broader class of field theories whose observables on a
spacetime are algebras over any single-colored operad. A novel feature of our
framework is that it gives rise to adjunctions between different types of field
theories. As an interesting example, we study an adjunction whose left adjoint
describes the quantization of linear field theories. We also analyze
homotopical properties of the linear quantization adjunction for chain complex
valued field theories, which leads to a homotopically meaningful quantization
prescription for linear gauge theories.
