We develop a denotational semantics of Linear Logic with least and greatest fixed points in a general categorical setting based on the notion of Seely category and on strong functors acting on them. We exhibit a simple instance of this setting in the category of sets and relations, where least and greatest fixed points are interpreted in the same way, and in a category of sets equipped with a notion of totality (non-uniform totality spaces) and relations preserving them, where least and greatest fixed points have distinct interpretations.

中文翻译：

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具有公式固定点的线性逻辑的分类模型

我们基于Seely类别的概念以及作用于它们的强函子，在一般的分类设置中开发了具有最小和最大不动点的线性逻辑的指称语义。我们在集合和关系的类别中展示此设置的一个简单实例，其中最小和最大不动点以相同的方式解释，并且在集合的类别中配备了总体（非一致总体空间）和关系的概念保存它们，最小和最大固定点有不同的解释。