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[Merged by Bors] - refactor(CategoryTheory/Sites): continuous functors #8408
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Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
I think that if we're introducing the name "This concept is also known as cocontinuous functors or This applies to the name continuous functor as well, but since we don't use that terminology for (co)limit preserving functors in mathlib, I think we can just remove that paragraph and claim both names for the sheaf-theoretic notion (and maybe add a warning that they don't mean "(co)limit-preserving". |
Could you also change line 44 in |
Thanks for the suggestions @dagurtomas! Now, there is |
Thanks 🎉 bors merge |
This PR introduces the typeclass `Functor.IsContinuous` which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem about `CoverPreserving` and `CompatiblePreserving` functors: it now states that such functors are continuous. The *pushforward* functor for a continuous functor is defined under the `Functor.IsContinuous` assumption rather than the combination of both `CoverPreserving` and `CompatiblePreserving`. The property `CoverLifting` is renamed `IsCocontinuous` and it is made a class. The property `IsCoverDense` is also made a class. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Build failed (retrying...): |
This PR introduces the typeclass `Functor.IsContinuous` which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem about `CoverPreserving` and `CompatiblePreserving` functors: it now states that such functors are continuous. The *pushforward* functor for a continuous functor is defined under the `Functor.IsContinuous` assumption rather than the combination of both `CoverPreserving` and `CompatiblePreserving`. The property `CoverLifting` is renamed `IsCocontinuous` and it is made a class. The property `IsCoverDense` is also made a class. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Build failed (retrying...): |
This PR introduces the typeclass `Functor.IsContinuous` which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem about `CoverPreserving` and `CompatiblePreserving` functors: it now states that such functors are continuous. The *pushforward* functor for a continuous functor is defined under the `Functor.IsContinuous` assumption rather than the combination of both `CoverPreserving` and `CompatiblePreserving`. The property `CoverLifting` is renamed `IsCocontinuous` and it is made a class. The property `IsCoverDense` is also made a class. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Build failed: |
retrying bors merge |
This PR introduces the typeclass `Functor.IsContinuous` which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem about `CoverPreserving` and `CompatiblePreserving` functors: it now states that such functors are continuous. The *pushforward* functor for a continuous functor is defined under the `Functor.IsContinuous` assumption rather than the combination of both `CoverPreserving` and `CompatiblePreserving`. The property `CoverLifting` is renamed `IsCocontinuous` and it is made a class. The property `IsCoverDense` is also made a class. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
Pull request successfully merged into master. Build succeeded: |
This PR introduces the typeclass `Functor.IsContinuous` which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem about `CoverPreserving` and `CompatiblePreserving` functors: it now states that such functors are continuous. The *pushforward* functor for a continuous functor is defined under the `Functor.IsContinuous` assumption rather than the combination of both `CoverPreserving` and `CompatiblePreserving`. The property `CoverLifting` is renamed `IsCocontinuous` and it is made a class. The property `IsCoverDense` is also made a class. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
This PR introduces the typeclass
Functor.IsContinuous
which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem aboutCoverPreserving
andCompatiblePreserving
functors: it now states that such functors are continuous. The pushforward functor for a continuous functor is defined under theFunctor.IsContinuous
assumption rather than the combination of bothCoverPreserving
andCompatiblePreserving
. The propertyCoverLifting
is renamedIsCocontinuous
and it is made a class. The propertyIsCoverDense
is also made a class.The current results are great, but I feel the terminology was very confusing: for example, the functor between categories of sheaves induced by a continuous functor was named
pullback
, even though it should be considered as a pushforward functor (for example, they induce the covariant functoriality of sheaves for sites or topological spaces). I have made some other similar renames.