On this page we have links to some terminology that cuts across different mathematical structures.

- extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties.
- extension
- equaliser (category)
- fixpoint
- order complete -
- complete (category) (Negation Complete) (directed complete partial orders dcpo) - A category is complete if every diagram in C has a limit in C. In order theory completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).
- canonicity - A type theory has canonicity if every term computes to a canonical form.
- preorder (set) (category) - A set with a binary relation which is reflexive and transitive.
- partial order
- poset
- axiom of choice
- classifier
- closure
- continuous
- exact functor
- generators
- Godels competeness theorem
- hom-set (category)
- inhabited
- kan extension (category)
- Lindenbaum Algebra
- natural number object
- powerset
- presheaf
- represention
- restriction
- section
- sieve
- weakly
- well founded
- well pointed