[Merged by Bors] - feat(CategoryTheory/MorphismProperty): HasPullbacksAgainst

[robin-carlier]

Given P P̀': MorphismProperty C, we add a type class HasPullbacksAgainst expressing that any morphism satisfying P admits a pullback along any morphism satisfying P'. We also add a type-class expressing that pullbacks of morphisms of P along any morphism satisfying P' still satisfies P.

This will be used to encode pairs of morphism properties for which suitable bicategories of spans exist.

From SymmMonCoherence

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I welcome any better name here! HasPullacksAlong and friends are already taken, hence I picked "against".

[github-actions]

PR summary 22853d3039

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ HasPullbacksAgainst
+ HasPushoutsAgainst
+ IsStableUnderBaseChangeAgainst
+ IsStableUnderCobaseChangeAgainst
+ _root_.CategoryTheory.Limits.hasPullback_ofHasPullbacksAgainst
+ _root_.CategoryTheory.Limits.hasPushout_ofHasPushoutsAgainst
+ hasPullbacksAgainst_top_iff
+ hasPushoutsAgainst_top_iff
+ instance (P : MorphismProperty C) [P.HasPullbacks] (P' : MorphismProperty C) :
+ instance (P : MorphismProperty C) [P.HasPushouts] (P' : MorphismProperty C) :
+ instance (P : MorphismProperty C) [P.IsStableUnderBaseChange]
+ instance (P : MorphismProperty C) [P.IsStableUnderCobaseChange]
+ isStableUnderBaseChangeAgainst_top_iff
+ isStableUnderCobaseChangeAgainst_top_iff

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

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No changes to strong technical debt.

No changes to weak technical debt.

[joelriou]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-CI job
• ci (staging) / Build
• ci (staging) / Lint style
• ci (staging) / Post-Build Step

[chrisflav]

This lemma does not seem to show what the name suggests (same below for hasPushoutsAgainst_top_iff).

[robin-carlier]

Oops, you’re right, it’s a copy-paste error. Fixed in #39647, thanks a lot for catching this!