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feat: CategoryTheory.toSheafify induces an isomorphism on stalks#35386

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Brian-Nugent:stalk_iso
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feat: CategoryTheory.toSheafify induces an isomorphism on stalks#35386
Brian-Nugent wants to merge 2 commits intoleanprover-community:masterfrom
Brian-Nugent:stalk_iso

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The main result TopCat.Presheaf.stalkFunctor_map_unit_toSheafify_isIso says that for a presheaf on a topological space, the induced map on stalks of CategoryTheory.toSheafify is an isomorphism. This is similar to TopCat.Presheaf.sheafifyStalkIso defined in the same file except that the latter is only for sheaves of Types.

The proof involved the abstract nonsense CategoryTheory.Adjunction.isIso_map_unit_of_isLeftAdjoint_comp which should probably go in a different file but feels too specific to go into any of the files in CategoryTheory.Adjunction.

Suggestions are very welcome.


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@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Feb 15, 2026
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@Brian-Nugent Brian-Nugent added t-category-theory Category theory t-topology Topological spaces, uniform spaces, metric spaces, filters t-algebraic-geometry Algebraic geometry labels Feb 15, 2026
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github-actions bot commented Feb 15, 2026

PR summary 33c03d9bba

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Topology.Sheaves.Sheafify 1040 1044 +4 (+0.38%)
Import changes for all files
Files Import difference
Mathlib.Topology.Sheaves.Sheafify 4

Declarations diff

+ isIso_map_unit_of_isLeftAdjoint_comp
+ map_unit_of_isLeftAdjoint_comp
+ skyscraperSheafForgetAdjunction
+ stalkFunctor_map_unit_toSheafify_isIso

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).

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new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! t-algebraic-geometry Algebraic geometry t-category-theory Category theory t-topology Topological spaces, uniform spaces, metric spaces, filters

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