Closed category of graded vector spaces

Let $(𝔄, +)$ be a monoid and $𝕂$ be a field. The closed category of $𝔄$ -graded vector spaces $𝗀 𝗋 𝔄 𝖵 𝖾 𝖼 𝗍 𝕂$ over $𝕂$ is the category where an object is a $𝔄$ -graded vector space and a morphism is a $𝕂$ -linear map, linalg closed monoidal so that $𝗀 𝗋 𝔄 𝖵 𝖾 𝖼 𝗍 𝕂 (𝑉, 𝑈)$ has a gradation given by ^homogenous maps. In particular, the endomorphism ring $E n d 𝕂 𝑉$ is a graded algebra.