More corrections under Tensor Product, and mention that monoids and bimodules between them form a bicategory, and that this construction can in turn be generalized to profunctors.

]]>Re #10:

This seems to originate in revision 36 from May 2022, part of about a dozen of anonymous edits.

]]>Yes.

]]>Oh, I wasn’t sure about that. Maybe you must define $A \otimes_{N} B$ as the coequalizer of $A \otimes \lambda^{B}, \rho^{A} \otimes B: A \otimes N \otimes B \rightarrow A \otimes B$?

]]>On the other hand, what you wrote isn’t what we normally understand by the tensor product of bimodules, either. It should be $A \otimes_N B$. I’ll come back to correct in a while, if no one else has.

]]>Oof. Thanks for pointing this out, J-B.

]]>There is a weird definition of tensor product of bimodules over rings in this entry. I think it’s not correct. (At least, I don’t think it’s the definition of the standard tensor product.)

]]>Added definition of tensor product of two bimodules over monoids in a monoidal category

]]>Added definition of a bimodule over a monoid in a monoidal category

]]>Are $R$-bimodules definable for non-associative unital integer algebras $R$? Current definitions only assume $R$ to be an associative unital integer algebra, but the definition of a Jordan superalgebra requires $R$ to not be associative.

]]>corrected typo. Sorry, I didn’t think that typos don’t require a comment.

]]>Added reference to module over a monad.

]]>Right, sorry, thanks for catching. Have removed it now.

]]>It’s a device Urs uses sometimes when editing, I think to remember where to begin again from after stopping. If it’s still there after some time, it can be deleted!

]]>I quote from the current entry:

Remark 4.2. As this notation suggests, $BMod_R$ is naturally the vertical category of a pseudo double category whose horizontal composition is given by tensor product of bimodules. spring

Does anyone know what the ’spring’ is doing at the end or should it be deleted?

]]>I noticed only now that the entry *bimodule* is in bad shape and needs some attention. For the moment I have added here a mentioning of the 2-category of algebras, bimodules and intertwiners and a pointer to the Eilenberg-Watts theorem.