We prove 2-categorical conservativity for any {0,T}-free fragment of MALL over its corresponding intuitionistic version: that is, that the universal map from a closed symmetric monoidal category to the *-autonomous category that it freely generates is fully faithful, and similarly for other doctrines. This implies that linear logics and graphical calculi for *-autonomous categories can also be interpreted canonically in closed symmetric monoidal categories. In particular, every closed symmetric monoidal category can be fully embedded in a *-autonomous category, preserving both tensor products and internal-homs. In fact, we prove this directly first with a Yoneda-style embedding (an enhanced "Hyland envelope" that can be regarded as a polycategorical form of Day convolution), and deduce 2-conservativity afterwards from Hyland-Schalk double gluing and a technique of Lafont. The same is true for other fragments of *-autonomous structure, such as linear distributivity, and the embedding can be enhanced to preserve any desired family of nonempty limits and colimits.
翻译:我们证明,对于MALL的任何 {0,T} 无差异的片段,我们对其相应的直觉论版进行2个分类保守:也就是说,从一个封闭的对称单相向类别到它自由产生的*自治类别,通用的地图是完全忠实的,与其他理论相似。这意味着,对于*自治类别的线性逻辑和图形计算器也可以在封闭的对称单相向类别中进行直截了当的解释。特别是,每个封闭的对称单相向类别都可以完全嵌入一个*自治类别,既保存高压产品,也保存内部合。事实上,我们首先证明这是由Yoneda式的嵌入式(一个强化的“湿地封”可被视为日进化的多种分类形式)直接的,然后从Hyland-Schaalk双曲线和拉弗坦技术推算出2个保守性。对于其他*自治结构的碎片,例如线性分裂性和内合性结构的碎片也是如此。事实上,我们首先证明了这一点,我们用一个Yoneda式的嵌入式嵌入式嵌入式嵌入式嵌入式(一个可被视为一种多类的“Hyland封状”的“Hyland封装”形式),可以被视为一种可被视为一种多式的“日变的“日变化”形式,从Hyculculturntration,然后推算出2-se。