In mathematics, a monoidal category (or tensor category) is a category
C
{\displaystyle \mathbf {C} }
equipped with a bifunctor
⊗
:
C
×
C
→
C
{\displaystyle \otimes :\mathbf {C} \times \mathbf {C} \to \mathbf {C} }
that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism. The associated natural ...
I have a question about Proposition 1.17 in Deligne and Milne, Tannakian Categories (see here), in the last 4 lines of the proof.
I don't why it follows from $U\otimes U\simeq U$ that $T=\ker(U\to U^\vee\otimes U)=0$ (or the largest subobject $T$ of $U$ such that $T\otimes U=0$ is $0$). Even ...
