A Note on Weak Algebraic Theories

Abstract : In our PhD thesis, we showed that for the study of denotational semantics of Linear Logic, it is crucial to generalize the standard notion of monad on a category. An earlier generalization was already given by Hoofman : semi-monads. But it was not suitable for our problem. This is why we introduced another generalization : weak monads. In this report, we present this new notion and give some examples.