Bundled exact functors #
We say that a functor F
is left exact if it preserves finite limits, it is right exact if it
preserves finite colimits, and it is exact if it is both left exact and right exact.
In this file, we define the categories of bundled left exact, right exact and exact functors.
Bundled left-exact functors.
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C ⥤ₗ D
denotes left exact functors C ⥤ D
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A left exact functor is in particular a functor.
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Bundled right-exact functors.
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C ⥤ᵣ D
denotes right exact functors C ⥤ D
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A right exact functor is in particular a functor.
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Bundled exact functors.
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C ⥤ₑ D
denotes exact functors C ⥤ D
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An exact functor is in particular a functor.
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Turn an exact functor into a left exact functor.
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Turn an exact functor into a left exact functor.
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Turn a left exact functor into an object of the category LeftExactFunctor C D
.
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Turn a right exact functor into an object of the category RightExactFunctor C D
.
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Turn an exact functor into an object of the category ExactFunctor C D
.