I am not particularly knowledgeable in either lambda calculus or category theory, but I am starting to learn Haskell so I would like to ask: are there connections between category theory and lambda calculus? Could anyone describe those connections in layman's terms?
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2One example might be the CurryHowardLambek correspondence, see e.g. [here](http://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence#Curry.E2.80.93Howard.E2.80.93Lambek_correspondence) and [here](http://www.haskell.org/haskellwiki/CurryHowardLambek_correspondence). – dtldarek Dec 02 '13 at 07:49

2One should be careful here which "lambda calculus" one has in mind. Simply typed lambda calculus is the natural internal language of cartesian closed categories. Unityped (aka untyped) is not. – Aleš Bizjak Dec 02 '13 at 08:10

1[This talk](https://www.youtube.com/watch?v=dgrucfgv2Tw) would be a very good answer to the question. – Boris Marinov May 02 '16 at 10:09
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Every model of a typed lambda calculus is a cartesian closed category.
Every cartesian closed category can be expressed as a typed lambda calculus (with the objects as types and arrows as terms).
Thus, typed lambda calculus and cartesian closed category are essentially the same concept.
Uday Reddy
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