free-categories: free categories

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free categories, paths, and categorical folds

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Dependencies base (>=4.12 && <=5) [details]
License BSD-3-Clause
Author Eitan Chatav
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Uploaded by echatav at 2019-10-01T17:38:51Z
Distributions LTSHaskell:, NixOS:, Stackage:
Reverse Dependencies 1 direct, 5 indirect [details]
Downloads 1485 total (26 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2019-10-01 [all 1 reports]

Readme for free-categories-

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Consider the category of Haskell "quivers" with

  • objects are types of higher kind
    • p :: k -> k -> Type
  • morphisms are terms of RankNType,
    • forall x y. p x y -> q x y
  • identity is id
  • composition is .

Now, consider the subcategory of Haskell Categorys with

  • constrained objects Category c => c
  • morphisms act functorially
    • t :: (Category c, Category d) => c x y -> d x y
    • t id = id
    • t (g . f) = t g . t f

The free category functor from quivers to Categorys may be defined up to isomorphism as

  • the functor Path of type-aligned lists

  • the functor FoldPath of categorical folds

  • abstractly as CFree path => path, the class of left adjoints to the functor which forgets the constraint on Category c => c

  • or as any isomorphic data structure