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1. • CommentRowNumber1.
   • CommentAuthorJohn Baez
   • CommentTimeMay 12th 2023
   • PermaLink
   Author: John Baez
   Format: MarkdownItexGave concrete formula for coextension of scalars and a case where extension and coextension agree. <a href="https://ncatlab.org/nlab/revision/diff/coextension+of+scalars/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/coextension+of+scalars/5">v5</a>, <a href="https://ncatlab.org/nlab/show/coextension+of+scalars">current</a>

   Gave concrete formula for coextension of scalars and a case where extension and coextension agree.

   diff, v5, current

2. • CommentRowNumber2.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 18th 2024
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   Author: nLab edit announcer
   Format: MarkdownItexSmall correction to the left action on $f_*(M)$. If S is not commutative then the multiplcation needs to be on the right. otherwise you get a right action instead of a left action Justin Desrochers <a href="https://ncatlab.org/nlab/revision/diff/coextension+of+scalars/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/coextension+of+scalars/9">v9</a>, <a href="https://ncatlab.org/nlab/show/coextension+of+scalars">current</a>

   Small correction to the left action on $f_*(M)$. If S is not commutative then the multiplcation needs to be on the right. otherwise you get a right action instead of a left action

   Justin Desrochers

   diff, v9, current

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeJun 19th 2024
   • (edited Jun 19th 2024)
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   Author: zskoda
   Format: MarkdownItexAt least (algebraic) geometers denote inverse image functor/extension of scalars by $f^*$, direct image functor/restriction of scalars by $f_*$ and its right adjoint by $f^!$. Because one wants to think of $f$ being in a geometric direction, that is opposite to the morphism of rings. Geometrically minded algebraists (and sheaf theorists) follow this convention as well.

   At least (algebraic) geometers denote inverse image functor/extension of scalars by $f^*$, direct image functor/restriction of scalars by $f_*$ and its right adjoint by $f^!$. Because one wants to think of $f$ being in a geometric direction, that is opposite to the morphism of rings. Geometrically minded algebraists (and sheaf theorists) follow this convention as well.