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Mathlib.Algebra.Category.AlgebraCat.Limits

The category of R-algebras has all limits #

Further, these limits are preserved by the forgetful functor --- that is, the underlying types are just the limits in the category of types.

The flat sections of a functor into AlgebraCat R form a submodule of all sections.

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    limit.π (F ⋙ forget (AlgebraCat R)) j as a AlgHom.

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      Construction of a limit cone in AlgebraCat R. (Internal use only; use the limits API.)

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        Witness that the limit cone in AlgebraCat R is a limit cone. (Internal use only; use the limits API.)

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          The forgetful functor from R-algebras to rings preserves all limits.

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          • AlgebraCat.forget₂RingPreservesLimits = AlgebraCat.forget₂RingPreservesLimitsOfSize

          The forgetful functor from R-algebras to R-modules preserves all limits.

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          • AlgebraCat.forget₂ModulePreservesLimits = AlgebraCat.forget₂ModulePreservesLimitsOfSize

          The forgetful functor from R-algebras to types preserves all limits.

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          • AlgebraCat.forgetPreservesLimits = AlgebraCat.forgetPreservesLimitsOfSize