 The analysis of self-reference and diagonalization has motivated the application of algebraic and topological techniques: consider Scott’s models for extensional lambda calculus (Scott 1972) and their subsequent categorical understanding. On the other hand, category theory has been used for new approaches to paradoxes since Lawvere 1969. A mathematical approach to the general issue of “self-reference vs. unfoundedness” can be found in Bernardi 2001, 2009. Besides Yablo’s paradox and a game theoretic version of Mirimanoff’s paradox, several classical results (existence of a non-r.e. set, Cantor’s theorems on the nondenumerability of the reals) can be transformed into existence theorems for suitable unfounded chains (and formally, unfounded chains are regarded as generalized fixed points).