In category theory, a branch of mathematics, an adequate subcategory of a category X is an analog of a dense subspace in topology for presheaves: namely, a subcategory such that the restriction of the Yoneda embedding along is still fully faithful.§ 2 in The notion was introduced by Isbell in 1960. Note some authors use the term dense subcategory for this notion, although it can mean a different thing in other contexts.
References
John Isbell, Adequate subcategories, Illinois J. Math. 4 (1960) pp. 541–552.
Further reading Dense subcategory