John Baez wrote:

>It's easy to make level slips in category theory, especially when discussing the category of categories, which is practically an invitation to make level slips.

To be fair, calling \$$\mathbf{Cat}\$$ a category is itself probably a level slip. My understanding from one of your papers you've shared in here is that \$$\mathbf{Cat}\$$ is something called a 2-category.