ACT@UCR Research Meeting: Quantifiers as Adjoints - Christian Williams

This is an introduction to the role of adjoints in categorical logic. The logical operations "or" and "and" are left adjoints of the diagonal map on propositions. More generally, existential and universal quantifiers can be seen as left and right adjoints to substitution. In a similar way, composition with a function between sets defines a functor between their slice categories that has both left and right adjoints. This in turn is a special case of how in any locally cartesian closed category, any morphism induces a functor between slice categories that has both left and right adjoints.

This talk on 2020 April 8 was part of the Applied Category Theory group meetings at U. C. Riverside.