Adequate subcategories

An adequate subcategory is a subcategory of a category such that maps whose domains are in the subcategory are adequate to determine every object of the category.  Dually, a coadequate subcategory is a subcategory such that maps whose codomains are in the subcategory are coadequate to determine every object in the category (Lawvere (1994) Tools for the advancement of objective logic: Closed categories and toposes, in The Logical Foundations of Cognition, J. Macnamara and G. E. Reyes (Eds). Oxford University Press, p. 49).