feat(category_theory/sites/*): Cover preserving functors #9650
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Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
…anprover-community/mathlib into cocontinuous_functor_on_sites
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Co-authored-by: Reid Barton <rwbarton@gmail.com>
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Split from #9650 - Defined `cover_preserving` functors as functors that push covering sieves to covering sieves. - Defined `compatible_preserving` functors as functors that push compatible families to compatible families. - Proved that functors that are both `cover_preserving` and `compatible_preserving` pulls sheaves to sheaves. Co-authored-by: erdOne <36414270+erdOne@users.noreply.github.com>
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Split from #9650 - Defined `cover_preserving` functors as functors that push covering sieves to covering sieves. - Defined `compatible_preserving` functors as functors that push compatible families to compatible families. - Proved that functors that are both `cover_preserving` and `compatible_preserving` pulls sheaves to sheaves. Co-authored-by: erdOne <36414270+erdOne@users.noreply.github.com>
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Split from #9650 - Defined `cover_preserving` functors as functors that push covering sieves to covering sieves. - Defined `compatible_preserving` functors as functors that push compatible families to compatible families. - Proved that functors that are both `cover_preserving` and `compatible_preserving` pulls sheaves to sheaves. Co-authored-by: erdOne <36414270+erdOne@users.noreply.github.com>
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Split from #9650 - Defined `cover_preserving` functors as functors that push covering sieves to covering sieves. - Defined `compatible_preserving` functors as functors that push compatible families to compatible families. - Proved that functors that are both `cover_preserving` and `compatible_preserving` pulls sheaves to sheaves. Co-authored-by: erdOne <36414270+erdOne@users.noreply.github.com>
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cover_preservingfunctors as functors that pushes covering sieves to covering sieves.representably_flatfunctors push compatiblefamily_of_elementsto compatible families.cover_preservingandrepresentably_flatpulls sheaves to sheaves.