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Theorems · Theorem · category theory

CategoryTheory.Limits.terminal.comp_from

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasTerminal C] {P Q : C}
  (f : P ⟶ Q),
  CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.terminal.from Q) = CategoryTheory.Limits.terminal.from P
Defined in
Mathlib.CategoryTheory.Limits.Shapes.Terminal
Cited by
21 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasTerminal

Around this declaration

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

HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence · cited by 4RightHomotopyClass.precom…HomotopicalAlgebra.isFibrant_iff_of_isTerminal · cited by 2HomotopicalAlgebra.isFibr…AlgebraicGeometry.AffineSpace.isPullback_map · cited by 2AffineSpace.isPullback_mapCategoryTheory.Dial.leftUnitor_hom_F · cited by 2Dial.leftUnitor_hom_FHomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinder · cited by 2LeftHomotopyRel.exists_ve…CategoryTheory.Dial.rightUnitor_hom_F · cited by 2Dial.rightUnitor_hom_FCategoryTheory.ObjectProperty.IsClosedUnderBinaryProducts.closedUnderIsomorphisms · cited by 2IsClosedUnderBinaryProduc…SSet.horn.IsCompatible.exists_lift_of_kanComplex · cited by 2IsCompatible.exists_lift_…CategoryTheory.Functor.relativelyRepresentable.of_diag · cited by 1relativelyRepresentable.o…HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map · cited by 1CofibrantObject.exists_bi…CategoryTheory.Functor.relativelyRepresentable.toPullbackTerminal · cited by 1relativelyRepresentable.t…HomotopicalAlgebra.FibrantObject.HoCat.exists_resolution_map · cited by 1HoCat.exists_resolution_m…CategoryTheory.Functor.relativelyRepresentable.diag_of_map_from_obj · cited by 1relativelyRepresentable.d…CategoryTheory.Dial.triangle · cited by 0Dial.triangleCategoryTheory.Limits.terminal.comp_from_assoc · cited by 0terminal.comp_from_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.HasTerminal · cited by 142Limits.HasTerminalCategoryTheory.Limits.terminal · cited by 141Limits.terminalCategoryTheory.Limits.terminal.from · cited by 77terminal.fromterminal.comp_fromCITED BYCITES

Cites6

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Cited by21

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