noun

• (uncountable) The joint direction of a film, organization, venture, etc.
  "Under the first of these, 5 collaborative research training fellowship projects were approved, on the following topics: stages of expansion of the railroads in Peru and their impact on its economy, under codirection of Heraclio Bonilla, Institute of Peruvian Sudies, Lima, and Marcello Carmagani, Luigi Einaudi Foundation, Turin Italy;..."
• (countable, mathematics) An equation for a hyperplane in the tangent space modulo a factor that is a positive constant; cotangent direction.
  "It can be shown that the set of hyperbolic codirections consists of distinct pairs of oppositely-directed convex cones."
• (uncountable, mathematics) Colinearity.