TeXipedia

simcoloncolon

Represents a double colon symbol with a tilde-like appearance, commonly used in mathematical notation for special relations or definitions.

Overview

Serves as a specialized mathematical notation symbol, particularly useful in advanced mathematics and theoretical computer science contexts where precise relation symbols are needed.

  • Often employed in category theory and abstract algebra to denote specific types of morphisms or mappings.
  • Used in formal logic and proof theory to indicate specialized definitional relationships.
  • Appears in mathematical texts where standard colons or double colons need visual distinction.

Examples

Expressing a binary relation in category theory.

F∼∷A→BF \simcoloncolon A \to B 
F \simcoloncolon A \to B

Denoting a type signature in type theory.

f∼∷X×Y→Zf \simcoloncolon X \times Y \to Z 
f \simcoloncolon X \times Y \to Z

Indicating a morphism between objects with additional structure.

ϕ∼∷(M,ω)→(N,η)\phi \simcoloncolon (M,\omega) \to (N,\eta) 
\phi \simcoloncolon (M,\omega) \to (N,\eta)