A. Kock. Strong functors and monoidal monads. Various Publications Series 11, Aarhus Universitet, August 1970. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Computational Lambda-Calculus and Monads - Moggi (1988) (272 citations) (Correct)
....strength t has to be given as an extra parameter for models. However, t is uniquely determined (but it may not exists) by T and the cartesian structure on C, when C has enough points, i.e. if f; g: A B, then f = g (8h: 1 A:h; f = h; g) The diagrams above are not new, they are all in [Koc70b], where a one one correspondence is established between functorial and tensorial strengths 6 : ffl the first two diagrams, saying that t is a tensorial strength of T , are (1.7) and (1.8) in [Koc70b] By Theorem 1.3 in [Koc70b] t induces a functorial strength of T making T a C enriched (also ....
....A B, then f = g (8h: 1 A:h; f = h; g) The diagrams above are not new, they are all in [Koc70b] where a one one correspondence is established between functorial and tensorial strengths 6 : ffl the first two diagrams, saying that t is a tensorial strength of T , are (1.7) and (1. 8) in [Koc70b]. By Theorem 1.3 in [Koc70b] t induces a functorial strength of T making T a C enriched (also called strong) functor. ffl the last two diagrams say that j and are natural transformations between suitable C enriched functors, namely j: Id C : T and : T 2 : T (see Remark 1.5 in [Koc70b] ....
[Article contains additional citation context not shown here]
A. Kock. Strong functors and monoidal monads. Various Publications Series 11, Aarhus Universitet, August 1970.
Computational Lambda-Calculus and Monads - Moggi (1988) (272 citations) (Correct)
....strength t has to be given as an extra parameter for models. However, t is uniquely determined (but it may not exists) by T and the cartesian structure on C, when C has enough points, i.e. if f; g: A B, then f = g (8h: 1 A:h; f = h; g) The diagrams above are not new, they are all in [Koc70b], where a one one correspondence is established between functorial and tensorial strengths 6 : the rst two diagrams, saying that t is a tensorial strength of T , are (1.7) and (1.8) in [Koc70b] By Theorem 1.3 in [Koc70b] t induces a functorial strength of T making T a C enriched (also ....
....g: A B, then f = g (8h: 1 A:h; f = h; g) The diagrams above are not new, they are all in [Koc70b] where a one one correspondence is established between functorial and tensorial strengths 6 : the rst two diagrams, saying that t is a tensorial strength of T , are (1.7) and (1. 8) in [Koc70b]. By Theorem 1.3 in [Koc70b] t induces a functorial strength of T making T a C enriched (also called strong) functor. the last two diagrams say that and are natural transformations between suitable C enriched functors, namely : Id C : T and : T 2 : T (see Remark 1.5 in [Koc70b] ....
[Article contains additional citation context not shown here]
A. Kock. Strong functors and monoidal monads. Various Publications Series 11, Aarhus Universitet, August 1970.
Types and Models for Higher-Order Action Calculi - Gardner, Hasegawa (1997) (2 citations) (Correct)
....work, a monad (T; j; satisfies the mono requirement if each component of j is a monomorphism. A tensorial strength for a monad T on a symmetric monoidal category is a natural transformation with components A;B : A Omega TB T (A Omega B) subject to the coherence conditions as found in [Koc70,Mog88,Mog91]. It is commutative if the evident two natural transformations from TA Omega TB to T (A Omega B) agree. Definition 37. A c model is a cartesian category C with a strong monad (T; j; which satisfies the mono requirement and has Kleisli exponents: that is, for each object A, the functor J ....
A. Kock, Strong functors and monoidal monads. Various Publications Series 11, Aarhus Universitet, 1970.
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