 | This article may be too technical for most readers to understand. (April 2022) |
A strong monad is a mathematical object defined using category theory that is used in theoretical computer science. In technical terms, a strong monad over a monoidal category (C, ⊗, I) is a monad (T, η, μ) together with a natural transformation tA,B : A ⊗ TB → T(A ⊗ B), called (tensorial) strength, such that the diagrams
, 
,
, and 
commute for every object A, B and C (see Definition 3.2 in [1]).
If the monoidal category (C, ⊗, I) is closed then a strong monad is the same thing as a C-enriched monad.
- ^ Moggi, Eugenio (July 1991). "Notions of computation and monads" (PDF). Information and Computation. 93 (1): 55–92. doi:10.1016/0890-5401(91)90052-4.