Kerodon

Remark 2.1.1.2. We will often abuse terminology by identifying a nonunital strict monoidal category $(\operatorname{\mathcal{C}}, \otimes )$ with the underlying category $\operatorname{\mathcal{C}}$. If we refer to a category $\operatorname{\mathcal{C}}$ as a nonunital strict monoidal category, we implicitly assume that $\operatorname{\mathcal{C}}$ has been endowed with a tensor product functor $\otimes : \operatorname{\mathcal{C}}\times \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}$ which is strictly associative in the sense of Definition 2.1.1.1.