Учитель Чистоты (maxim) wrote in category_theory,
Учитель Чистоты
maxim
category_theory

MONADS NEED NOT BE ENDOFUNCTORS

We will elsewhere comment on the relation of our relative monads to the recent gen- eralization of monads by Spivey [31] that was also motivated by programming examples: he fixes a functor K ∈ C → J (notice the direction) to then look for monad-like structures with an underlying functor J → C. With Paul Levy we have checked that a fair amount of monad theory transfers to his generalized monads, but they are not monoids in [J, C] unless K has a left adjoint, in which case they are equivalent to relative monads. Sam Staton has considered an enriched variant of relative monads.

http://jmchapman.github.io/papers/relmon-lmcs.pdf
Tags: monads, revisited
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