Timeline for Categorical presentation of direct sums of vector spaces, versus tensor products
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2020 at 14:34 | comment | added | Jake Wetlock | Thanks, this explanation actually makes more sense to me! | |
| Dec 21, 2020 at 23:27 | comment | added | Qiaochu Yuan | Instead of talking about multilinear maps directly we can also talk about the fact that the set $[V, W]$ of linear maps between two vector spaces is itself a vector space, which produces a closed category structure on $\text{Vect}$. Then we can ask for a left adjoint satisfying a tensor-hom adjunction $\text{Hom}(V_1 \otimes V_2, W) \cong \text{Hom}(V_1, [V_2, W])$. The connection to multilinear maps being that both of these functors describe bilinear maps $V_1 \times V_2 \to W$. | |
| Dec 21, 2020 at 0:59 | vote | accept | Jake Wetlock | ||
| Dec 21, 2020 at 0:50 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
deleted 7 characters in body
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| Dec 21, 2020 at 0:08 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |