TY - JOUR
T1 - Distributivity for endofunctors, pointed and co-pointed endofunctors, monads and comonads
AU - Lenisa, M
AU - Power, John
AU - Watanabe, H
PY - 2000
Y1 - 2000
N2 - We generalise the notion of a distributive law between a monad and a comonad to consider weakened structures such as pointed or co-pointed endofunctors, or endofunctors. We investigate Eilenberg-Moore and Kleisli constructions for each of these possibilities. Then we consider two applications of these weakened notions of distributivity in detail. We characterise Turi and Plotkin's model of GSOS as a distributive law of a monad over a co-pointed endofunctor, and we analyse generalised coiteration and coalgebraic coinduction “up-to” in terms of a distributive law of the underlying pointed endofunctor of a monad over an endofunctor.
AB - We generalise the notion of a distributive law between a monad and a comonad to consider weakened structures such as pointed or co-pointed endofunctors, or endofunctors. We investigate Eilenberg-Moore and Kleisli constructions for each of these possibilities. Then we consider two applications of these weakened notions of distributivity in detail. We characterise Turi and Plotkin's model of GSOS as a distributive law of a monad over a co-pointed endofunctor, and we analyse generalised coiteration and coalgebraic coinduction “up-to” in terms of a distributive law of the underlying pointed endofunctor of a monad over an endofunctor.
UR - http://dx.doi.org/10.1016/S1571-0661(05)80350-0
U2 - 10.1016/S1571-0661(05)80350-0
DO - 10.1016/S1571-0661(05)80350-0
M3 - Article
SN - 1571-0661
VL - 33
SP - 230
EP - 260
JO - Electronic Notes in Theoretical Computer Science
JF - Electronic Notes in Theoretical Computer Science
ER -