Theorems · Theorem · category theory

HomotopicalAlgebra.isFibrant_iff_of_isTerminal

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.CategoryWithFibrations C]
  [inst_2 : CategoryTheory.Limits.HasTerminal C] [(HomotopicalAlgebra.fibrations C).RespectsIso] {X Y : C} (p : X ⟶ Y)
  (hY : CategoryTheory.Limits.IsTerminal Y), HomotopicalAlgebra.IsFibrant X ↔ HomotopicalAlgebra.Fibration p

Defined in

Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithFibrationsCategoryTheory.Limits.HasTerminalCategoryTheory.MorphismProperty.RespectsIso