UniMath

This coq library aims to formalize a substantial body of mathematics using the univalent point of view.

View the Project on GitHub UniMath/UniMath

UniMath uses both ASCII and Unicode notation. Below we give an overview of the most important symbols. To see how to input a specific Unicode character, type C-u C-x = (meaning: hold CTRL, then press u and x; release CTRL, press =) while hovering over that character.

Below is a partial list of Unicode symbols and identifiers used in UniMath.

Item UniMath symbol Unicode input UniMath ASCII alternative
Type and term constructors      
Product type ∏ (x : A), B \prod forall x : A, B
Function type A → B \to A -> B
Lambda abstraction λ x, e \lambda fun x => e
Sigma type ∑ (x : A), B \sum total2 (fun x => B)
Cartesian product type X × Y \times dirprod X Y
Pair term a,,b   a,,b
Coproduct type X ⨿ Y \union then select from menu coprod X Y
Identity type a = b   a = b
Univalent logic in hProp      
Conjunction A ∧ B \and hconj A B
Disjunction A ∨ B \or hdisj A B
Implication A ⇒ B \=> himpl A B
Negation ¬ X \neg hneg X
Universal quantification ∀ x , P x \forall forall_hProp A
Existential quantification ∃ x, P x \ex hexists P
Propositional truncation ∥ A ∥ \\|\| ishinh A
Category theory      
Object type of C ob C or C    
Morphisms C⟦a,b⟧ \[[ and \]] a --> b
Functor F on objects F a    
Functor F on morphisms #F f