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 such that the restriction of the Yoneda embedding along is still fully faithful.[1] The notion was introduced by Isbell in 1960. Note some authors[2] use the term dense subcategory for this notion, although it can mean a different thing in other contexts.

References

  1. ^ § 2 in Lawvere, F. W. (2002). "Metric spaces, generalized logic and closed categories" (PDF). Reprints in Theory and Applications of Categories (1): 1–37.
  2. ^ Lurie, Jacob. "Kerodon". kerodon.net. Retrieved 2026-03-18.
  • John Isbell, Adequate subcategories , Illinois J. Math. 4 (1960) pp. 541–552. [1]

Further reading

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