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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeJun 11th 2023
   • PermaLink
   Author: zskoda
   Format: MarkdownItexA stub for a notion *different* from [[twisted tensor product]] of a dg-algebra with a dg-coalgebra, which has a previously existing entry. <a href="https://ncatlab.org/nlab/revision/twisted+tensor+product+of+algebras/1">v1</a>, <a href="https://ncatlab.org/nlab/show/twisted+tensor+product+of+algebras">current</a>

   A stub for a notion different from twisted tensor product of a dg-algebra with a dg-coalgebra, which has a previously existing entry.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 11th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexYou should define the term "$R$-ring", this is non-standard terminology, as far as I am aware. I see that Orlov introduces it on his [p. 8](https://arxiv.org/pdf/2305.19799.pdf#page=8), but it remains unclear to me why he can't just consider any $R$-algebras.

   You should define the term “$R$-ring”, this is non-standard terminology, as far as I am aware. I see that Orlov introduces it on his p. 8, but it remains unclear to me why he can’t just consider any $R$-algebras.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2023
   • (edited Jun 12th 2023)
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   Author: zskoda
   Format: MarkdownItex$R$-rings and $R$-corings are rather standard objects in modern algebra. Maybe we can just give a pointer to section in $n$Lab about $R$-rings: <https://ncatlab.org/nlab/show/ring#rings_over_a_ring_rings> Orlov explains somewhere that the case when $R$ is not in a center is needed for his (derived algebraic geometry) purposes.

   $R$-rings and $R$-corings are rather standard objects in modern algebra. Maybe we can just give a pointer to section in $n$Lab about $R$-rings: https://ncatlab.org/nlab/show/ring#rings_over_a_ring_rings

   Orlov explains somewhere that the case when $R$ is not in a center is needed for his (derived algebraic geometry) purposes.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2023
   • (edited Jun 12th 2023)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWe can separate the section "rings over a ring" to a separate entry (like corings have). Rings over $R\otimes R^{op}$ are very much used in bialgebroid theory, since Takeuchi. (This is why source and target map appear in role of a unit.)

   We can separate the section “rings over a ring” to a separate entry (like corings have).

   Rings over $R\otimes R^{op}$ are very much used in bialgebroid theory, since Takeuchi. (This is why source and target map appear in role of a unit.)

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Maybe we can just give a pointer to section in nLab about R-rings: Absolutely.

   Maybe we can just give a pointer to section in nLab about R-rings:

   Absolutely.