Timeline for Gamma spaces and monoidal categories II
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2012 at 2:31 | comment | added | Geoffroy Horel | What you do is adding a disjoint unit or equivalently writing you non unital monoid as the augmentation kernel of an augmented monoid. I can tell you what happens for commutative algebras in the category of chain complexes. I don't know how relevant it is to this situation. So if A is an augmented algebra and I is its augmentation ideal, then the iterated bar $B^n(A)$ is equivalent to $k\oplus B^n(I)[n]$. You can find this result in a paper of Po Hu. | |
| Mar 2, 2012 at 20:18 | comment | added | Ulrich Pennig | Thank you. That makes sense. I also wondered about the following thing: I could just add a dummy object 1 to the category with mor(1,x) = empty if x is not 1 and mor(1,1) = id_1. Is there any problem with extending the monoidal structure in such a way that 1 becomes a unit? If this works: What is the relation between the delooping above and the delooping of the "unification"? | |
| Mar 2, 2012 at 15:29 | history | answered | Geoffroy Horel | CC BY-SA 3.0 |