nLab higher-level foundations

Higher-level foundations




The basis of it all

 Set theory

set theory

Foundational axioms

foundational axiom

Removing axioms


Higher-level foundations


By higher-level foundations, or simply higher foundations, we mean any foundation of mathematics in which there are, or at least can be, basic objects of h-level higher than h-sets. Thus, these objects behave like groupoids or infinity-groupoids (or even categories or infinity-categories). This is in contrast to set-level foundations such as set theory and set-level type theory in which all objects behave like sets.

Some higher-level foundations include:

Last revised on November 28, 2022 at 18:29:48. See the history of this page for a list of all contributions to it.