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@ncfavier
Last active June 14, 2024 13:42
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adjunction yoga 🧘

L ⊣ R

adjunct : (L a β†’ b) β†’ (a β†’ R b)
coadjunct : (a β†’ R b) β†’ (L a β†’ b)
unit : a β†’ RL a
counit : LR b β†’ b
Lmap : (a β†’ b) β†’ (L a β†’ L b)
Rmap : (a β†’ b) β†’ (R a β†’ R b)

adjunct f = unit ; Rmap f
coadjunct f = Lmap f ; counit
unit = adjunct id
counit = coadjunct id
Lmap f = coadjunct (f ; unit)
Rmap f = adjunct (counit ; f)

https://ncatlab.org/nlab/show/geometry+of+physics+%E2%80%93+basic+notions+of+category+theory#ReExpressingMiddleFunctorInAdjointTriple

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