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Step * 1 1 of Lemma monad-of-Kleisli-adjunction


1. C : SmallCategory
2. M : Monad(C)
3. x : cat-ob(C)@i
⊢ (monad-functor(adjMonad(Kl(C;M))) x) = (monad-functor(M) x) ∈ cat-ob(C)
BY
{ (RepUR ``adjunction-monad monad-functor mk-monad`` 0
   THEN RepUR ``Kleisli-left Kleisli-right functor-comp`` 0
   THEN Fold `monad-functor` 0
   THEN Fold `monad-fun` 0
   THEN Auto) }

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Latex:

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Latex:

1.  C  :  SmallCategory
2.  M  :  Monad(C)
3.  x  :  cat-ob(C)@i
\mvdash{}  (monad-functor(adjMonad(Kl(C;M)))  x)  =  (monad-functor(M)  x)


By

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Latex:
(RepUR  ``adjunction-monad  monad-functor  mk-monad``  0
  THEN  RepUR  ``Kleisli-left  Kleisli-right  functor-comp``  0
  THEN  Fold  `monad-functor`  0
  THEN  Fold  `monad-fun`  0
  THEN  Auto)

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