We currently have enough machinary to (kind of) define Betti numbers (for homology see Floris van Doorn's thesis ). I am confident that soon we can start compting Betti numbers of some types. This would allow us to define the euler characterstic E : U --> N of a type. If classical algebraic topology tells us anything this will satisfy a lot of neat identities. In fact consider U as a semiring with + and * as the operations. E is a semiring homomorphism to N (the initial semiring (is this relavent?)). In other words we should have E(X + Y) = E(X) + E(Y) E(X * Y) = E(X) E(Y) and even maybe, subject to some conditions, a given type family P : X --> U would satisfy E( (x : X) * P(x) ) = E(X) * E(P(x_0)) This would be a cool invariant to have. Unfortunately as it stands, homology is a bit unwieldy. Perhaps rationalising spaces would help? Any thoughts or suggestions? -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout.