Mathlib v3 is deprecated. Go to Mathlib v4

Commit 2021-10-04 08:10 6a6b4d05

View on Github →

feat(category_theory/sites/*): Cover-lifting functors on sites (#9431) This PR defines cover-liftings functors between sites, and proves that Ran F.op maps sheaves to sheaves for cover-lifting functors F. This will probably be needed when we want to glue B-sheaves into sheaves.

Estimated changes

Created src/category_theory/sites/cover_lifting.lean

added def category_theory.Ran_is_sheaf_of_cover_lifting.get_section

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.get_section_commute

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.get_section_is_amalgamation

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.get_section_is_unique

added def category_theory.Ran_is_sheaf_of_cover_lifting.glued_limit_cone

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.glued_limit_cone_π_app

added def category_theory.Ran_is_sheaf_of_cover_lifting.glued_section

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.glued_section_is_amalgamation

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.glued_section_is_unique

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.helper

added def category_theory.Ran_is_sheaf_of_cover_lifting.pulledback_family

added theorem category_theory.Ran_is_sheaf_of_cover_lifting.pulledback_family_apply

added theorem category_theory.Ran_is_sheaf_of_cover_lifting

added def category_theory.comp_cover_lifting

added structure category_theory.cover_lifting

added def category_theory.id_cover_lifting

Modified src/category_theory/sites/sheaf_of_types.lean

modified def category_theory.SheafOfTypes

added def category_theory.presieve.family_of_elements.comp_presheaf_map

added theorem category_theory.presieve.family_of_elements.compatible.comp_presheaf_map

added theorem category_theory.presieve.family_of_elements.compatible.functor_pullback

added theorem category_theory.presieve.family_of_elements.compatible.pullback

added def category_theory.presieve.family_of_elements.functor_pullback

added def category_theory.presieve.family_of_elements.pullback

Modified src/category_theory/sites/sieves.lean

added def category_theory.presieve.functor_pullback

added theorem category_theory.presieve.functor_pullback_id

added theorem category_theory.presieve.functor_pullback_mem

modified def category_theory.sieve.functor

added def category_theory.sieve.functor_pullback

added theorem category_theory.sieve.functor_pullback_id

modified structure category_theory.sieve

Modified src/category_theory/structured_arrow.lean

added def category_theory.structured_arrow.hom_mk'