  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.
