  Lawvere from early on promoted the idea that a category of categories could be used as a foundational framework. (See Lawvere 1964, 1966.) This proposal now rests in part on the development of higher-dimensional categories, also called weak \(n\)-categories. (See, for instance Makkai 1998.) The advent of topos theory in the seventies brought new possibilities. Mac Lane has suggested that certain toposes be considered as a genuine foundation for mathematics. (See Mac Lane 1986.) Lambek proposed the so-called free topos as the best possible framework, in the sense that mathematicians with different philosophical outlooks might nonetheless agree to adopt it. (See Couture &amp; Lambek 1991, 1992, Lambek 1994.) He has also argued that there is no topos that can thoroughly satisfy a classical mathematician. (See Lambek 2004.) (For more on the various foundational views among category theorists, see Landry &amp; Marquis 2005.)