Theorems · Theorem · category theory

CategoryTheory.IsPullback.of_isLimit_binaryFan_of_isTerminal

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} {c : CategoryTheory.Limits.BinaryFan X Y}
  (hc : CategoryTheory.Limits.IsLimit c) {T : C} (hT : CategoryTheory.Limits.IsTerminal T),
  CategoryTheory.IsPullback c.fst c.snd
    (hT.from ((CategoryTheory.Limits.pair X Y).obj { as := CategoryTheory.Limits.WalkingPair.left }))
    (hT.from ((CategoryTheory.Limits.pair X Y).obj { as := CategoryTheory.Limits.WalkingPair.right }))

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category