Theorems · Theorem · category theory
CategoryTheory.Limits.PreservesFiniteProducts.of_exponentialIdeal
∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₁, u₂} D]
(i : CategoryTheory.Functor D C) [inst_2 : CategoryTheory.CartesianMonoidalCategory C]
[inst_3 : CategoryTheory.Reflective i] [inst_4 : CategoryTheory.MonoidalClosed C]
[CategoryTheory.CartesianMonoidalCategory D] [CategoryTheory.ExponentialIdeal i] [CategoryTheory.BraidedCategory C],
CategoryTheory.Limits.PreservesFiniteProducts (CategoryTheory.reflector i)If a reflective subcategory is an exponential ideal, then the reflector preserves finite products.
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- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Limits.WalkingPairproof · cited by 1,319
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
- CategoryTheory.Limits.PreservesLimitsOfShapeproof · cited by 156
- CategoryTheory.MonoidalClosedstatement and proof · cited by 134
- CategoryTheory.Limits.PreservesFiniteProductsstatement · cited by 75
- CategoryTheory.Reflectivestatement and proof · cited by 27
- CategoryTheory.reflectorstatement and proof · cited by 17
- CategoryTheory.ExponentialIdealstatement and proof · cited by 8
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