Provide details for extensivity proofs - #313
Merged
Merged
Conversation
ScriptRaccoon
force-pushed
the
extensive-explanation
branch
3 times, most recently
from
July 29, 2026 12:25
b7a2c2c to
48297a7
Compare
…ot infinitary distributive, hence not infinitary extensive
ScriptRaccoon
force-pushed
the
extensive-explanation
branch
from
July 29, 2026 16:04
b82922a to
b3ef277
Compare
ScriptRaccoon
force-pushed
the
extensive-explanation
branch
from
July 30, 2026 05:36
b3ef277 to
62cd567
Compare
ScriptRaccoon
marked this pull request as ready for review
July 30, 2026 05:36
… form consistently
ScriptRaccoon
changed the title
This file contains hidden or 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
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
This PR fixes #112 by adding more details to the proofs that various categories are extensive (or infinitary extensive or coextensive). So far, these were merely proof sketches, and several arguments were missing. The definitions of these properties have also been improved.
The proof for Meas was actually incorrect and has been corrected. This category is merely countably extensive, not infinitary extensive as previously claimed, because it is not infinitary distributive.
To clarify the proofs for Man, Setc, and Meas, the property "countably extensive" and its dual have been added to the database. This seems natural since we already have "countably distributive" and "countable coproducts" in the database. The two new properties have been decided for all categories without any additional effort.
Another small change (unrelated to extensivity): The category Setf has been renamed to Setff (ff = finite fibers). Some authors denote the category of finite sets by Setf, and "ff" is a bit more descriptive, so this removes some ambiguity.