Hello, 1) In the very last chapter (Session 33 "2: Toposes and logic" of "Conceptual Mathematics" where the authors cover topoi, they define '=>' for the internal Heyting algebra of Omega: "Another logical operation is 'implication', which is denoted '=>'. This is also a map Omega x Omega->Omega, defined as the classifying map of the subobject S 'hook' Omega x Omega determined by the all those <alpha, beta> in Omega x Omega such that alpha "subset of" beta." Starting from "subobject S 'hook" ......" I got totally lost. I am frustrated because I know this is crucial to understanding why Omega is an internal Heyting algebra, so any help would be appreciated. (I am assuming that alpha and beta are subojects of Omega???). 2) In the same Session 33 on pg 350 is a set "rules of logic". These are exactly the axioms for a Heyting algebra, yes? Regards, Bill Halchin