Theorems · Theorem · category theory

CategoryTheory.Limits.hasLimit_iff_hasTerminal_cone

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
  (F : CategoryTheory.Functor J C),
  CategoryTheory.Limits.HasLimit F ↔ CategoryTheory.Limits.HasTerminal (CategoryTheory.Limits.Cone F)

Defined in: Mathlib.CategoryTheory.Limits.ConeCategory
Cited by: 1 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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Cites13

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

DFunLike.coeproof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
Equiv.symmproof · cited by 3,681
CategoryTheory.Limits.Conestatement and proof · cited by 710
CategoryTheory.Limits.HasLimitstatement and proof · cited by 226
CategoryTheory.Limits.limit.isLimitproof · cited by 146
CategoryTheory.Limits.HasTerminalstatement and proof · cited by 142
CategoryTheory.Limits.terminalproof · cited by 141
CategoryTheory.Limits.limit.coneproof · cited by 97
CategoryTheory.Limits.terminalIsTerminalproof · cited by 31
CategoryTheory.Limits.IsTerminal.hasTerminalproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.hasLimitsOfShape_iff_isLeftAdjoint_constproof · cited by 2