mathlib documentation

category_theory.preadditive.left_exact

Left exactness of functors between preadditive categories #

We show that a functor is left exact in the sense that it preserves finite limits, if it preserves kernels. The dual result holds for right exact functors and cokernels.

Main results #

A functor between preadditive categories preserves the equalizer of two morphisms if it preserves all kernels.

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A functor between preadditive categories which preserves kernels preserves all finite limits.

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A functor between preadditive categoris preserves the coequalizer of two morphisms if it preserves all cokernels.

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A functor between preadditive categories which preserves kernels preserves all finite limits.

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