6 Matching Annotations
  1. Feb 2021
    1. Though rarer in computer science, one can use category theory directly, which defines a monad as a functor with two additional natural transformations. So to begin, a structure requires a higher-order function (or "functional") named map to qualify as a functor:

      rare in computer science using category theory directly in computer science What other areas of math can be used / are rare to use directly in computer science?

    1. It's hard to say why people think so because you certainly don't need to know category theory for using them, just like you don't need it for, say, using functions.
  2. Jul 2020
  3. Jan 2020
  4. Jun 2018
    1. Remark1.73.IfPandQare total orders andf:P!Qand1:Q!Pare drawn witharrows bending as in Exercise 1.72, we believe thatfis left adjoint to1iff the arrows donot cross. But we have not proved this, mainly because it is difficult to state precisely,and the total order case is not particularly general