Timeline for On the derived functor of the tensor product in a monoidal category
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2021 at 15:14 | vote | accept | Adrien MORIN | ||
| Oct 5, 2021 at 16:32 | comment | added | Dmitri Pavlov | @AdrienMORIN: Yes, the underlying object of Q is cofibrant as an object of M. | |
| Oct 5, 2021 at 16:32 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Oct 5, 2021 at 16:32 | comment | added | Dmitri Pavlov | @AdrienMORIN: If you have two cofibrant replacements Q and Q' of the monoid 1 in Mon(M), they are connected by a zigzag of weak equivalences Q→Q''←Q' in Mon(M). This zigzag induces a zigzag of weak equivalences of lax monoidal functors, as constructed in the answer. | |
| Oct 5, 2021 at 14:47 | comment | added | Adrien MORIN | Could you comment a bit about the last part of my question, i.e. whether the derived structures one obtains through different cofibrant replacements of 1 in Mon(M) are essentially the same ? I suppose it somehow comes from the "homotopical uniqueness" of cofibrant replacements ? | |
| Oct 5, 2021 at 14:19 | comment | added | Adrien MORIN | Do you mean "the underlying object $Q$ is a cofibrant object of $M$" ? | |
| Oct 4, 2021 at 17:01 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |