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feat(CategoryTheory/Sites): the fiber functor associated to Point.comap#35722

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feat(CategoryTheory/Sites): the fiber functor associated to Point.comap#35722
joelriou wants to merge 7 commits intoleanprover-community:masterfrom
joelriou:comap-pullback

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@joelriou joelriou commented Feb 24, 2026

The definition Point.comap is moved to a separate file. Using results on skyscraper sheaves, we obtain that if F : C ⥤ D is a representably flat continuous functor between sites (C, J) and (D, K), Φ is a point of (D, K), then the fiber functor attached to the point Φ.comap F hF of the site (C, J) (where hF : CoverPreserving J K F) identifies to the composition of the pullback functor for F followed by the fiber functor attached to the point Φ. This is a generalization to arbitrary sites of https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sheaves/Stalks.html#TopCat.Presheaf.stalkPullbackIso

Co-authored-by: Christian Merten


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@joelriou joelriou added WIP Work in progress t-category-theory Category theory labels Feb 24, 2026
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PR summary 360d94e7b3

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.CategoryTheory.Sites.Point.Skyscraper (new file) 1145
Mathlib.CategoryTheory.Sites.Point.Comap (new file) 1147

Declarations diff

+ isSheaf_skyscraperPresheaf
+ isSheaf_skyscraperPresheaf_aux
+ piFunctor
+ sheafFiberComapIso
+ sigmaFunctor
+ skyscraperPresheaf
+ skyscraperPresheafAdjunction
+ skyscraperPresheafFunctor
+ skyscraperPresheafHomEquiv
+ skyscraperPresheafHomEquiv_app_π
+ skyscraperPresheafHomEquiv_naturality_left_symm
+ skyscraperPresheafHomEquiv_naturality_right
+ skyscraperSheaf
+ skyscraperSheafAdjunction
+ skyscraperSheafFunctor
+ skyscraperSheafFunctorCompSheafPushforwardContinuous
+ toPresheafFiber_skyscraperPresheafHomEquiv_symm

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@joelriou joelriou changed the title feat(CategoryTheory/Sites): the fiber functors associated to Point.comap feat(CategoryTheory/Sites): the fiber functor associated to Point.comap Feb 24, 2026
@mathlib-dependent-issues mathlib-dependent-issues bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Feb 24, 2026
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