Category Theory Illustrated – Types

chromacity

It's a great introduction, but I find the premise a bit funny. It starts with Russell's paradox, insinuates that solving it within set theory makes set theory complex (it doesn't, you basically just restrict what can be used to build a set), and then introduces a system that is fundamentally more complex .

layer8

Regarding Russell’s paradox, its dual is also interesting: Consider the set D := { s | s ∈ s }, the set of sets that do contain themselves. Does D contain itself? It might or it might not, neither causes a contradiction. Tnis shows that you don’t need an antinomy for a set comprehension to be ill-defined.

Koshkin

> a set can contain itself Can it? > a term can have only one type... Due to this law, types cannot contain themselves Doesn't look like one follows from the other...