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Commit 2022-03-04 15:24 e41303d6

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feat(category_theory/limits/shapes): preserving (co)kernels (#12419) This is work towards showing that homology is a lax monoidal functor.

Estimated changes

Modified src/category_theory/limits/is_limit.lean

added def category_theory.limits.is_colimit.equiv_of_nat_iso_of_iso

added def category_theory.limits.is_limit.equiv_of_nat_iso_of_iso

Modified src/category_theory/limits/preserves/shapes/equalizers.lean

Created src/category_theory/limits/preserves/shapes/kernels.lean

added def category_theory.limits.is_colimit_cofork_map_of_is_colimit'

added def category_theory.limits.is_colimit_map_cocone_cofork_equiv'

added def category_theory.limits.is_colimit_of_has_cokernel_of_preserves_colimit

added def category_theory.limits.is_limit_fork_map_of_is_limit'

added def category_theory.limits.is_limit_map_cone_fork_equiv'

added def category_theory.limits.is_limit_of_has_kernel_of_preserves_limit

added def category_theory.limits.preserves_cokernel.iso

added theorem category_theory.limits.preserves_cokernel.iso_hom

added def category_theory.limits.preserves_cokernel.of_iso_comparison

added def category_theory.limits.preserves_kernel.iso

added theorem category_theory.limits.preserves_kernel.iso_hom

added def category_theory.limits.preserves_kernel.of_iso_comparison

Modified src/category_theory/limits/shapes/equalizers.lean

added def category_theory.limits.parallel_pair.ext

Modified src/category_theory/limits/shapes/kernels.lean

added def category_theory.limits.cokernel_comparison

added theorem category_theory.limits.cokernel_comparison_map_desc

added def category_theory.limits.cokernel_is_cokernel

added def category_theory.limits.kernel_comparison

added theorem category_theory.limits.kernel_comparison_comp_π

added def category_theory.limits.kernel_is_kernel

added theorem category_theory.limits.map_lift_kernel_comparison

added theorem category_theory.limits.ι_comp_cokernel_comparison