kb/data/en.wikipedia.org/wiki/Adequate_subcategory-0.md

title	chunk	source	category	tags	date_saved	instance
Adequate subcategory	1/1	https://en.wikipedia.org/wiki/Adequate_subcategory	reference	science, encyclopedia	2026-05-05T13:38:46.918580+00:00	kb-cron

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
    ↪
    X
  

{\displaystyle i:A\hookrightarrow X}

such that the restriction of the Yoneda embedding

    X
    ↪
    
      P
    
    (
    X
    )
  

{\displaystyle X\hookrightarrow \mathbf {P} (X)}

along

    i
  

{\displaystyle 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. [1]

== Further reading == Dense subcategory