It looks like you're new here. If you want to get involved, click one of these buttons!

- All Categories 2.4K
- Chat 505
- Study Groups 21
- Petri Nets 9
- Epidemiology 4
- Leaf Modeling 2
- Review Sections 9
- MIT 2020: Programming with Categories 51
- MIT 2020: Lectures 20
- MIT 2020: Exercises 25
- Baez ACT 2019: Online Course 339
- Baez ACT 2019: Lectures 79
- Baez ACT 2019: Exercises 149
- Baez ACT 2019: Chat 50
- UCR ACT Seminar 4
- General 75
- Azimuth Code Project 111
- Statistical methods 4
- Drafts 10
- Math Syntax Demos 15
- Wiki - Latest Changes 3
- Strategy 113
- Azimuth Project 1.1K
- - Spam 1
- News and Information 148
- Azimuth Blog 149
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 719

Options

## Comments

Monoidal unit is 1.

The \( * \) operation is associative and commutative, so it satisfies properties (c) and (d).

Multiplication of any \( x \in \mathbb{N} \) by 1 yields back \(x\), so (b) holds as well.

Multiplication by any \(z \in \mathbb{N}\) in \( (\mathbb{N}, \leq) \) is monotone, i.e. it holds that for any \( x, y \in \mathbb{N} \), if \( x \leq y \) then \( x * z \leq y * z \), so (a) is satisfied as well and \( (\mathbb{N}, \leq, 1, *) \) is a symmetric monoidal preorder.

`Monoidal unit is 1. The \\( * \\) operation is associative and commutative, so it satisfies properties (c) and (d). Multiplication of any \\( x \in \mathbb{N} \\) by 1 yields back \\(x\\), so (b) holds as well. Multiplication by any \\(z \in \mathbb{N}\\) in \\( (\mathbb{N}, \leq) \\) is monotone, i.e. it holds that for any \\( x, y \in \mathbb{N} \\), if \\( x \leq y \\) then \\( x * z \leq y * z \\), so (a) is satisfied as well and \\( (\mathbb{N}, \leq, 1, *) \\) is a symmetric monoidal preorder.`