Steps and traces

Abstract In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, Kleisli category a monad or its Eilenberg–Moore category. This paper elaborates two new unifying ideas: (i) coalgebraic,draftrules is naturally presented terms corecursive algebras, and (ii) all three approaches arise as instances same abstract setting. Our perspective puts different under common roof allows to derive conditions which some them coincide.