Theorems · Theorem · category theory
CategoryTheory.PreGaloisCategory.card_fiber_coprod_eq_sum
∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] (F : CategoryTheory.Functor C FintypeCat)
[inst_1 : CategoryTheory.PreGaloisCategory C] [CategoryTheory.PreGaloisCategory.FiberFunctor F] (X Y : C),
Nat.card (F.obj (X ⨿ Y)).obj = Nat.card (F.obj X).obj + Nat.card (F.obj Y).objThe cardinality of the fiber of a coproduct is the sum of the cardinalities of the fibers.
- Defined in
- Mathlib.CategoryTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Equivproof · cited by 8,337
- CategoryTheory.Functor.compproof · cited by 6,529
- Finitestatement · cited by 3,029
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CategoryTheory.Iso.symmproof · cited by 993
- Nat.cardstatement and proof · cited by 844
- CategoryTheory.Iso.transproof · cited by 566
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