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Theorems · Theorem · category theory

CategoryTheory.Limits.IsTerminal.comp_from

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Z : C} (t : CategoryTheory.Limits.IsTerminal Z) {X Y : C}
  (f : X ⟶ Y), CategoryTheory.CategoryStruct.comp f (t.from Y) = t.from X
Defined in
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
Cited by
13 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst · cited by 24CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd · cited by 16CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_hom_fst · cited by 8CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fst · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd · cited by 6CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_inv_snd · cited by 6CartesianMonoidalCategory…HomotopicalAlgebra.isFibrant_iff_of_isTerminal · cited by 2HomotopicalAlgebra.isFibr…CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.isFiltered · cited by 1IndizationClosedUnderFilt…CategoryTheory.Limits.IsTerminal.isCardinalFiltered · cited by 1IsTerminal.isCardinalFilt…CategoryTheory.Limits.isIso_of_isTerminal · cited by 1Limits.isIso_of_isTerminalSkyscraperPresheafFunctor.map'_comp · cited by 0SkyscraperPresheafFunctor…SSet.quasicategory_iff_of_isTerminal · cited by 0SSet.quasicategory_iff_of…CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminal · cited by 0IsPullback.of_isLimit_bin…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.IsTerminal.hom_ext · cited by 29IsTerminal.hom_extIsTerminal.comp_fromCITED BYCITES

Cites6

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Cited by13

Results whose statement or proof uses this declaration.