Two results on finite categories#137
Merged
ScriptRaccoon merged 2 commits intomainfrom Apr 27, 2026
Merged
Conversation
this was already in the database, but then was "improved" to => finitely accessible, which however is not dualized, since we do not have finitely coaccessible.
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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 back the implication "finite + cauchy complete => filtered colimits", which was in the DB before, but was replaced with the stronger statement "finite + cauchy complete => finitely accessible" (in #97). The problem is that the stronger statement is not dualized automatically since "finitely accessible" has no dual in the database (as of now). So we have both "versions" now, and the first one is dualized automatically to "finite + cauchy complete => cofiltered limits".
Also, this PR adds the result "finite + cauchy complete => monos are stable under filtered colimits" (which is also dualized automatically). As a consequence, two manual assignments could be removed (and also another one in a PR in progress, #136).
💭 Let's make it a rule from now on to always add the dual property as well when a new property is added. Only then the deduction system works to its full power.