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I am looking for a reference for the following statement. Theorem. Let $C$ be a regular, well-powered, countably complete cartesian closed category, $R$ be a (commutative) ring object in $C$, $R\...

Let $C$ be a monoidal closed category with tensor $\otimes$ and internal hom $[-, -]$. Suppose that $C$ acts by adjoint monads, i.e. $- \otimes X$ is a comonad and $[X, -]$ is a monad, and each $F : ...

In a closed symmetric monoidal category with $[I,X] \cong X$ for all $X$ is it true that having monomorphisms $m :A \rightarrow B$ and $m: B \rightarrow A$ is enough to imply $A \cong B$ ? I tried to ...