Draft

• multigraph

• quiver graph: directed multigraph, 有向伪图

• quiver, loop arrows from and to the same vertex

• object, vertex in a graph

• from directed multigraph to categories

• morphism, or arrow

• identity morphism

• composition of morphisms

• There can be multiple different loops on one object, but one of them must be the identity morphism. Why?

• endofunctor

• Haskell languge is a category, Hask, with the Haskell language types as the objects and Haskell-langauge functions are morphisms.

• 'Hask' is a Cartesian closed category

• n-category

• monoids for input and output in Haskell language

Topics

• Haskell and WL

• category theory and WL

References

• Bartosz Milewsk, "Category Theory for Programmers," 2014 - 2017, https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/.
• Eugenia Cheng's research papers on category theory
• 'TheCatsters' Youtube channel
  • Brent Yorgey's index to 'TheCatsters' videos
• Tom Leinster, "Basic Category Theory," 2016, arXiv:1612.09375v1 [math.CT]
• Tom Leinster's research papers