Dan wrote:

> My take is that \\(\mathbf{Bool}\\)-enriched categories are preorders, but they are not monoidal.

Right. There's nothing in the definition of enriched category that gives a way to multiply objects, so there's nothing "monoidal" about them. In the next lecture I'll show a \\(\mathbf{Bool}\\)-enriched category is a preorder, nothing more and nothing less.

Later we will meet _monoidal_ enriched categories, but we're not there yet!

> My take is that \\(\mathbf{Bool}\\)-enriched categories are preorders, but they are not monoidal.

Right. There's nothing in the definition of enriched category that gives a way to multiply objects, so there's nothing "monoidal" about them. In the next lecture I'll show a \\(\mathbf{Bool}\\)-enriched category is a preorder, nothing more and nothing less.

Later we will meet _monoidal_ enriched categories, but we're not there yet!