We develop a denotational semantics of muLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional muMALL with exponentials. Our general categorical setting is based on the notion of Seely category and on strong functors acting on them. We exhibit two simple instances of this setting. In the first one, which is based on the category of sets and relations, least and greatest fixed points are interpreted in the same way. In the second one, based on a category of sets equipped with a notion of totality (non-uniform totality spaces) and relations preserving them, least and greatest fixed points have distinct interpretations. This latter model shows that muLL enjoys a denotational form of normalization of proofs.

翻译：我们开发了一种术语术语词义的MULL(MULL),即一种最起码和最大的定点版本,用指数来延伸David Baelde的标本模模模模模L(MULL),我们的一般直截了当的设置基于Seelly类别的概念和根据这些类别行事的强力杀菌者。我们展示了两种简单的例子。在第一种基于组别和关系类别,最小和最大的定点被以同样的方式解释。在第二种假设中,基于一个组别,装备了整体(非统一的完整空间)概念和保持它们的关系,最小和最大的固定点有不同的解释。后一种模型表明,MULLL享有证据正常化的隐喻形式。