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

**Cost**-categories)? How do we interpret this in terms of distances?

## Comments

In a Lawvere metric space, \(I=0\). So, an identity element is a map \(\mathrm{id}_x:0\to\mathcal{X}(x,x)\). In terms of distances, this means that \(0\geq d(x,x)\) (since \(0\) is the smallest element of \([0,\infty]\), this means \(d(x,x)=0\) (this was already observed in the text between the definition of a Lawvere metric space as a

Cost-category and the example of \(\mathbb{R}\) as a Lawvere metric space, in chapter 2), which is the statement of definiteness for a Lawvere metric).`In a Lawvere metric space, \\(I=0\\). So, an identity element is a map \\(\mathrm{id}_x:0\to\mathcal{X}(x,x)\\). In terms of distances, this means that \\(0\geq d(x,x)\\) (since \\(0\\) is the smallest element of \\([0,\infty]\\), this means \\(d(x,x)=0\\) (this was already observed in the text between the definition of a Lawvere metric space as a **Cost**-category and the example of \\(\mathbb{R}\\) as a Lawvere metric space, in chapter 2), which is the statement of definiteness for a Lawvere metric).`