Small groupoids are generalized varieties and finitely accessible#195
Merged
Conversation
ScriptRaccoon
changed the title
ScriptRaccoon
changed the title
ScriptRaccoon
force-pushed
the
groupoids-generalized-varieties
branch
from
97d95cf to
f9cb3ec
Compare
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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 adds the (easy) proof that every essentially small groupoid is a generalized variety, and also finitely accessible.
This result brings the number of unknown properties for B (finite sets and bijections) and the two entries of BG down to zero.
This result also makes it possible to remove the assignments that 0 and 2 are multi-algebraic, which are now redundant: they are multi-cocomplete, and are small groupoids, hence generalized varieties, and hence multi-algebraic.