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Theorems · Definition · category theory

CategoryTheory.Coverage.toPrecoverage

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] → CategoryTheory.Coverage C → CategoryTheory.Precoverage C
Defined in
Mathlib.CategoryTheory.Sites.Coverage
Cited by
33 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Coverage.toGrothendieck · cited by 15Coverage.toGrothendieckCategoryTheory.Presieve.isSheaf_coverage · cited by 8Presieve.isSheaf_coverageCategoryTheory.Coverage.toGrothendieck_toPrecoverage · cited by 4Coverage.toGrothendieck_t…CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpi · cited by 4regularTopology.mem_sieve…CategoryTheory.coherentTopology.mem_sieves_iff_hasEffectiveEpiFamily · cited by 3coherentTopology.mem_siev…CategoryTheory.over_toGrothendieck_eq_toGrothendieck_comap_forget · cited by 3CategoryTheory.over_toGro…CategoryTheory.Coverage.mem_toGrothendieck_sieves_of_superset · cited by 2Coverage.mem_toGrothendie…CategoryTheory.Coverage.pullback · cited by 2Coverage.pullbackCategoryTheory.extensive_regular_generate_coherent · cited by 2CategoryTheory.extensive_…CategoryTheory.Precoverage.isSheaf_toGrothendieck_iff_of_isStableUnderBaseChange · cited by 1Precoverage.isSheaf_toGro…CategoryTheory.Precoverage.toCoverage_toPrecoverage · cited by 1Precoverage.toCoverage_to…CategoryTheory.Presheaf.isSheaf_iff_isLimit_coverage · cited by 1Presheaf.isSheaf_iff_isLi…CategoryTheory.Coverage.ext · cited by 1Coverage.extCategoryTheory.Coverage.generates_toGrothendieck · cited by 1Coverage.generates_toGrot…CategoryTheory.extensiveTopology.mem_sieves_iff_contains_colimit_cofan · cited by 1extensiveTopology.mem_sie…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Precoverage · cited by 204CategoryTheory.PrecoverageCategoryTheory.Coverage · cited by 31CategoryTheory.CoverageCoverage.toPrecoverageCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by37

Results whose statement or proof uses this declaration.