Category Theory

Category Theory

This package is part of the Axle domain specific language.

A very simple example with Objects, Arrows, and a Category.

      import axle.category.awodey.CategoryTheory._

      val ints = ⋅(Set(1, 2))
      val strings = ⋅(Set("A", "B"))

      println("ints ≡ strings: " + (ints ≡ strings))
      println("ints ≡ ints   : " + (ints ≡ ints))

      val fii = →(ints, ints) /* TODO */
      val fis = →(ints, strings) /* TODO */
      val fsi = →(strings, ints) /* TODO */
      val fss = →(strings, strings) /* TODO */

      println("fii ≡ fii: " + (fii ≡ fii))
      println("fii ≡ fis: " + (fii ≡ fis))

      // val setsFin1 = Category(Set(ints, strings), Set(fii, fis, fsi, fss))
      val setsFin1 = Category(Set(ints), Set(fii))

See the wikipedia page on Category Theory for some more background.