nLab notions of subcategory

• subcategory

  • full, wide, dense, replete

  • reflective, coreflective, bireflective

  • abelian, Serre, topologizing

  • internal subcategory

  • dense sub-site

• sub-2-category

  • full sub-2-category

  • locally full sub-2-category

  • reflective sub-2-category

• localizing subcategory

• sub-(∞,1)-category (internal formulation)

  • reflective sub-(∞,1)-category (internal formulation)

  • reflective product-preserving sub-(∞,1)-category (internal formulation)

• thick subcategory (of a triangulated category)

• block decomposition of a category

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