an algebraic quantum field theory $\AAA\in\AQFT$ is additive, one can consider its underlying functor $\AAA : \Loc\to \CC$ to the category $\CC$ (i.e. forget the algebra structures) and equivalently check if $\colim\big(\AAA\vert_M : \RC_M\to\CC\big)\to \AAA(M)$ is an isomorphism in $\CC$.

Furthermore, we introduce a suitable local constancy property that is also known in the literature as the time-slice axiom.

\[def:AQFTCauchyconstant\] An algebraic quantum field theory $\AAA\in\AQFT$ is called [*Cauchy constant*]{} if $\AAA(f) :\AAA(M)\to \AAA(N)$ is an isomorphism in $\Alg$, for every Cauchy morphism $f: M\stackrel{c}{\to} N$. We denote by $\AQFT^c\subseteq \AQFT$ the full subcategory of Cauchy constant algebraic quantum field theories. The full subcategory $\AQFT^{\addc}\subseteq \AQFT^\add$ of Cauchy constant additive algebraic quantum field theories is defined analogously.

\[sec:construction\]From PFA to AQFT
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In this section we show that every Cauchy constant additive prefactorization algebra $\FFF\in\PFA^{\addc}$ (cf. Definitions \[def:additivePFA\] and \[def:CauchyconstantPFA\]) defines a Cauchy constant additive algebraic quantum field theory (cf. Definitions \[def:AQFTadditive\] and \[def:AQFTCauchyconstant\]). This construction will define a functor $\bbA : \PFA^{\addc} \to \AQFT^{\addc}$.

Our construction consists of three steps, which will be carried out in detail in individual subsections below. Step (1) consists of proving that, for each $M\in\Loc$, the object $\FFF(M)\in\CC$ carries canonically the structure of an 