I've added some puzzles to the end of today's lecture:

**Puzzle 90.** What's a \\(\mathbf{Cost}^{\text{op}}\\)-category, and what if anything are they good for?

Some of you have already answered the first part. Section 2.3.4 of the book leads you through other examples of enriched categories. Here's another. Let

\[ D = \\{ \textrm{Monday}, \textrm{Tuesday}, \textrm{Wednesday}, \textrm{Thursday}, \textrm{Friday}, \textrm{Saturday}, \textrm{Sunday} \\} \]

and let

\[ \mathcal{V} = \prod_{d \in D} \mathbf{Cost} \]

that is, the product of 7 copies of \\(\mathbf{Cost}\\), one for each day of the week.

**Puzzle 91.** Show how to make the product of symmetric monoidal posets into a symmetric monoidal poset. Thus, \\(\mathcal{V} \\) becomes a symmetric monoidal poset. What is a \\(\mathcal{V} \\)-category like, and what are they good for in everyday life?

**Puzzle 90.** What's a \\(\mathbf{Cost}^{\text{op}}\\)-category, and what if anything are they good for?

Some of you have already answered the first part. Section 2.3.4 of the book leads you through other examples of enriched categories. Here's another. Let

\[ D = \\{ \textrm{Monday}, \textrm{Tuesday}, \textrm{Wednesday}, \textrm{Thursday}, \textrm{Friday}, \textrm{Saturday}, \textrm{Sunday} \\} \]

and let

\[ \mathcal{V} = \prod_{d \in D} \mathbf{Cost} \]

that is, the product of 7 copies of \\(\mathbf{Cost}\\), one for each day of the week.

**Puzzle 91.** Show how to make the product of symmetric monoidal posets into a symmetric monoidal poset. Thus, \\(\mathcal{V} \\) becomes a symmetric monoidal poset. What is a \\(\mathcal{V} \\)-category like, and what are they good for in everyday life?