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

- All Categories 2.3K
- Chat 499
- Study Groups 18
- Petri Nets 9
- Epidemiology 3
- Leaf Modeling 1
- Review Sections 9
- MIT 2020: Programming with Categories 51
- MIT 2020: Lectures 20
- MIT 2020: Exercises 25
- MIT 2019: Applied Category Theory 339
- MIT 2019: Lectures 79
- MIT 2019: Exercises 149
- MIT 2019: Chat 50
- UCR ACT Seminar 4
- General 67
- Azimuth Code Project 110
- Statistical methods 3
- Drafts 2
- Math Syntax Demos 15
- Wiki - Latest Changes 3
- Strategy 113
- Azimuth Project 1.1K
- - Spam 1
- News and Information 147
- Azimuth Blog 149
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 708

Options

References to John's lectures: lecture 9.

I had some trouble making this one, repeatedly drawing things I later realized were false. The key realization for me was that everything hinges on the possible presence of "non-injective" and "non-surjective" elements in the codomain. With that understanding, I think I got the pictures correct.

Given how many mistakes I made, you may want to be extra-wary about trusting the details on this one : )

EDIT: And I did indeed have a big misunderstanding of how \(h_*\) works. I've updated with corrections and improvements.

*Revision history:*

*- 2018 06 18: Fixed errors in definition of \(h_*\). Better pictures and explanations of the adjunction behavior.*

*- 2018 05 26: First version.*

## Comments

`![picture](https://i.imgur.com/N9qjEpJ.png)`