Adequate subcategory

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 $i:A\hookrightarrow X$ such that the restriction of the Yoneda embedding $X\hookrightarrow \mathbf {P} (X)$ along $i$ is still fully faithful. 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