[Merged by Bors] - feat(CategoryTheory): naturality of the connecting homomorphism of the snake lemma #8490
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
leanprover-community-mathlib4-bot
added
the
blocked-by-other-PR
This was referenced Nov 18, 2023
leanprover-community-mathlib4-bot
removed
the
blocked-by-other-PR
|
This PR/issue depends on: |
jcommelin
approved these changes
Nov 28, 2023
Comment on lines
+32
to
+36
| `L₀.X₁ ⟶ L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁ ⟶ L₃.X₂ ⟶ L₃.X₃`. Each of the four exactness | ||
| statement is first stated separately as lemmas `L₀_exact`, `L₁'_exact`, | ||
| `L₂'_exact` and `L₃_exact` and the full 6-term exact sequence is stated | ||
| as `snake_lemma`. This sequence can even be extended with an extra `0` | ||
| on the left (see `mono_L₀_f`) if `L₁.X₁ ⟶ L₁.X₂` is a mono (i.e. `L₁` is short exact), |
There was a problem hiding this comment.
Suggested change
| `L₀.X₁ ⟶ L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁ ⟶ L₃.X₂ ⟶ L₃.X₃`. Each of the four exactness | |
| statement is first stated separately as lemmas `L₀_exact`, `L₁'_exact`, | |
| `L₂'_exact` and `L₃_exact` and the full 6-term exact sequence is stated | |
| as `snake_lemma`. This sequence can even be extended with an extra `0` | |
| on the left (see `mono_L₀_f`) if `L₁.X₁ ⟶ L₁.X₂` is a mono (i.e. `L₁` is short exact), | |
| `L₀.X₁ ⟶ L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁ ⟶ L₃.X₂ ⟶ L₃.X₃`. Each of the four exactness | |
| statements is first stated separately as lemma `L₀_exact`, `L₁'_exact`, | |
| `L₂'_exact` and `L₃_exact` and the full 6-term exact sequence is stated | |
| as `snake_lemma`. This sequence can even be extended with an extra `0` | |
| on the left (see `mono_L₀_f`) if `L₁.X₁ ⟶ L₁.X₂` is a mono (i.e. `L₁` is short exact), |
leanprover-community-mathlib4-bot
added
ready-to-merge
mathlib-bors bot
pushed a commit
that referenced
this pull request
Nov 28, 2023
…e snake lemma (#8490) In this PR, it is shown that the connecting homomorphism of the snake lemma is natural.
|
Pull request successfully merged into master. Build succeeded: |
mathlib-bors
bot
changed the title
awueth
pushed a commit
that referenced
this pull request
Dec 19, 2023
…e snake lemma (#8490) In this PR, it is shown that the connecting homomorphism of the snake lemma is natural.
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
In this PR, it is shown that the connecting homomorphism of the snake lemma is natural.