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1. • CommentRowNumber1.
   • CommentAuthorsamwinnick
   • CommentTimeAug 30th 2022
   • (edited Aug 30th 2022)
   • PermaLink
   Author: samwinnick
   Format: MarkdownItexI'm a little confused by the wording of the internalized definition of ideal here. What exactly is meant here by the composite ${S\otimes A\otimes S\to S\otimes S\otimes S\to S}$ factoring through ${i:A\to S}$? Don't we need something like, for all $A\to S\otimes A\otimes S$ the relevant diagram commutes? Is this what is meant? --- The "discuss this page" link on the page [[ideal in a monoid]] doesn't work, I guess because the discussion thread hadn't been created yet, so I created this post through the n-forum.

   I’m a little confused by the wording of the internalized definition of ideal here. What exactly is meant here by the composite ${S\otimes A\otimes S\to S\otimes S\otimes S\to S}$ factoring through ${i:A\to S}$? Don’t we need something like, for all $A\to S\otimes A\otimes S$ the relevant diagram commutes? Is this what is meant?

   ---

   The “discuss this page” link on the page ideal in a monoid doesn’t work, I guess because the discussion thread hadn’t been created yet, so I created this post through the n-forum.