[Merged by Bors] - feat: Monoidal and cartesian distributive categories#20182
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[Merged by Bors] - feat: Monoidal and cartesian distributive categories#20182
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Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
…nprover-community/mathlib4 into sina-distributive-categories
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
…nprover-community/mathlib4 into sina-distributive-categories
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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This PR defines monoidal and cartesian distributive categories, develop the API, and prove some main results. We show a closed monoidal category is distributive. We also show that, for a category `C` with binary coproducts, the category of endofunctors `C ⥤ C` is left distributive. This requires the following new file which develops a convenient API for the binary (co)products in the functor categories: CategoryTheory/Limits/FunctorCategory/Shapes/BinaryProducts In Mathlib/CategoryTheory/Distributive/Cartesian.lean we show that the coproduct coprojections are monic in a cartesian distributive category.
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This PR defines monoidal and cartesian distributive categories, develop the API, and prove some main results. We show a closed monoidal category is distributive. We also show that, for a category `C` with binary coproducts, the category of endofunctors `C ⥤ C` is left distributive. This requires the following new file which develops a convenient API for the binary (co)products in the functor categories: CategoryTheory/Limits/FunctorCategory/Shapes/BinaryProducts In Mathlib/CategoryTheory/Distributive/Cartesian.lean we show that the coproduct coprojections are monic in a cartesian distributive category.
idontgetoutmuch
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…unity#20182) This PR defines monoidal and cartesian distributive categories, develop the API, and prove some main results. We show a closed monoidal category is distributive. We also show that, for a category `C` with binary coproducts, the category of endofunctors `C ⥤ C` is left distributive. This requires the following new file which develops a convenient API for the binary (co)products in the functor categories: CategoryTheory/Limits/FunctorCategory/Shapes/BinaryProducts In Mathlib/CategoryTheory/Distributive/Cartesian.lean we show that the coproduct coprojections are monic in a cartesian distributive category.
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This PR defines monoidal and cartesian distributive categories, develop the API, and prove some main results. We show a closed monoidal category is distributive.
We also show that, for a category
Cwith binary coproducts, the category of endofunctorsC ⥤ Cis left distributive. This requires the following new file which develops a convenient API for the binary (co)products in the functor categories:CategoryTheory/Limits/FunctorCategory/Shapes/BinaryProducts
In Mathlib/CategoryTheory/Distributive/Cartesian.lean we show that the coproduct coprojections are monic in a cartesian distributive category.