nLab
regular logic

Definition

Regular logic is the internal logic of regular categories. Its logical operations consist only of truth, conjunction, and existential quantification, which makes it a superset of finite-limit logic and a subset of coherent logic and geometric logic.

Related concepts

• finitely complete category, cartesian functor, cartesian logic, cartesian theory

• regular category, regular functor, regular logic, regular theory, regular coverage, regular topos

• coherent category, coherent functor, coherent logic, coherent theory, coherent coverage, coherent topos

• geometric category, geometric functor, geometric logic, geometric theory

References

Section 4.2 of

• Jaap van Oosten, Basic category theory (pdf)

Section D1.2 of

• Peter Johnstone, Sketches of an Elephant