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Theorems · Definition · category theory

HomotopicalAlgebra.FibrantObject

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [HomotopicalAlgebra.CategoryWithFibrations C] → [CategoryTheory.Limits.HasTerminal C] → Type u

The full subcategory of fibrant objects.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.Bifibrant
Cited by
21 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithFibrationsCategoryTheory.Limits.HasTerminal

Around this declaration

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

HomotopicalAlgebra.FibrantObject.homRel · cited by 12FibrantObject.homRelHomotopicalAlgebra.FibrantObject.mk · cited by 10FibrantObject.mkHomotopicalAlgebra.FibrantObject.homMk · cited by 8FibrantObject.homMkHomotopicalAlgebra.FibrantObject.toHoCat · cited by 8FibrantObject.toHoCatHomotopicalAlgebra.FibrantObject.ι · cited by 2FibrantObject.ιHomotopicalAlgebra.BifibrantObject.ιFibrantObject · cited by 2BifibrantObject.ιFibrantO…HomotopicalAlgebra.FibrantObject.HoCat.resolution · cited by 2HoCat.resolutionHomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObject · cited by 2HoCat.ιFibrantObjectHomotopicalAlgebra.FibrantObject.homMk_homMk · cited by 1FibrantObject.homMk_homMkHomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_src · cited by 1FibrantObject.homRel_equi…HomotopicalAlgebra.FibrantObject.homRel_iff_leftHomotopyRel · cited by 1FibrantObject.homRel_iff_…HomotopicalAlgebra.FibrantObject.localizerMorphism · cited by 1FibrantObject.localizerMo…HomotopicalAlgebra.FibrantObject.toHoCat_map_eq · cited by 1FibrantObject.toHoCat_map…HomotopicalAlgebra.BifibrantObject.ιFibrantObjectLocalizerMorphism · cited by 1BifibrantObject.ιFibrantO…HomotopicalAlgebra.FibrantObject.HoCat.localizerMorphismResolution · cited by 1HoCat.localizerMorphismRe…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…CategoryTheory.Limits.HasTerminal · cited by 142Limits.HasTerminalHomotopicalAlgebra.CategoryWithFibrations · cited by 46HomotopicalAlgebra.Catego…HomotopicalAlgebra.fibrantObjects · cited by 20HomotopicalAlgebra.fibran…HomotopicalAlgebra.FibrantObj…CITED BYCITES

Cites5

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

Cited by40

Results whose statement or proof uses this declaration.