by oriented and time-oriented globally hyperbolic Lorentzian manifolds, i.e. on the case of relativistic quantum field theory, and disregard until Section \[subsec:Involutions\] the $\ast$-involutions on algebraic quantum field theories because prefactorization algebras are usually considered without a concept of $\ast$-involution. Our main result is an equivalence theorem between (Cauchy constant and additive) algebraic quantum field theories and (Cauchy constant, additive and time-orderable) prefactorization algebras, cf. Theorem \[theo:equivalence\]. Our equivalence theorem is considerably more general than the earlier comparison result by Gwilliam and Rejzner [@GwilliamRejzner]: (1) We work in a model-independent setup, supplemented by natural additional hypotheses such as Cauchy constancy, additivity and time-orderability, while [@GwilliamRejzner] only studies linear quantum field theories, such as e.g. the free Klein-Gordon field. (2) We investigate in detail uniqueness, associativity, naturality and Einstein causality of the multiplications $\mu_M : \FFF(M)\otimes\FFF(M)\to \FFF(M)$ determined by a Cauchy constant additive prefactorization algebra $\FFF$, which requires rather sophisticated arguments from Lorentzian geometry. These questions were not addressed in [@GwilliamRejzner]. (3) Our equivalence theorem admits an interpretation in terms of operad theory (cf. Remark \[rem:operad\]), which provides a suitable starting point for generalizations to higher categorical quantum field theories [@CostelloGwilliam; @BSShocolim; @BSfibered; @BSWhomotopy; @BSoverview] such as gauge theories. (The present 