  Motivated by the recent interest in models of guarded (co-)recursion, we
study their equational properties. We formulate axioms for guarded fixpoint
operators generalizing the axioms of iteration theories of Bloom and \'Esik.
Models of these axioms include both standard (e.g., cpo-based) models of
iteration theories and models of guarded recursion such as complete metric
spaces or the topos of trees studied by Birkedal et al. We show that the
standard result on the satisfaction of all Conway axioms by a unique dagger
operation generalizes to the guarded setting. We also introduce the notion of
guarded trace operator on a category, and we prove that guarded trace and
guarded fixpoint operators are in one-to-one correspondence. Our results are
intended as first steps leading, hopefully, towards future description of
classifying theories for guarded recursion.
