CatDat

• Notation: $(\Cat,\times,1)$
• Underlying category: category of small categories
• Related symmetric monoidal categories: $(\Set,\times,1)$
• nLab Link

Every category with finite products (also called a cartesian category) can be endowed with a symmetric monoidal structure, where $1$ is the terminal object and $\otimes$ is the product $\times$. In this case, we apply this to the category $\Cat$ of small categories.