We analyze quantum field theories on spacetimes $M$ with timelike boundaryfrom a model-independent perspective. We construct an adjunction whichdescribes a universal extension to the whole spacetime $M$ of theories definedonly on the interior $\mathrm{int}M$. The unit of this adjunction is a naturalisomorphism, which implies that our universal extension satisfies Kay'sF-locality property. Our main result is the following characterization theorem:Every quantum field theory on $M$ that is additive from the interior (i.e.\generated by observables localized in the interior) admits a presentation by aquantum field theory on the interior $\mathrm{int}M$ and an ideal of itsuniversal extension that is trivial on the interior. We shall illustrate ourconstructions by applying them to the free Klein-Gordon field.
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机译：我们从模型独立的角度分析了具有时空边界的时空$ M $的量子场论。我们构造一个附加函数，该附加函数描述对仅在内部$ \ mathrm {int} M $上定义的理论的整个时空$ M $的通用扩展。该附加的单位是自然同构，这意味着我们的通用扩展满足Kay的F-局部性。我们的主要结果是下面的刻画定理：每个关于$ M $的量子场论，都是从内部（即\\由位于内部的可观察对象生成的）加成的，它接受了量子场论对内部\\ mathrm {int}的表示。 M $及其在内部通用的扩展性理想。我们将通过将其应用于免费的Klein-Gordon字段来说明我们的构造。
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