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

- All Categories 2.2K
- Applied Category Theory Course 356
- Applied Category Theory Seminar 4
- Exercises 149
- Discussion Groups 50
- How to Use MathJax 15
- Chat 482
- Azimuth Code Project 108
- News and Information 145
- Azimuth Blog 149
- Azimuth Forum 29
- Azimuth Project 189
- - Strategy 108
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 711
- - Latest Changes 701
- - - Action 14
- - - Biodiversity 8
- - - Books 2
- - - Carbon 9
- - - Computational methods 38
- - - Climate 53
- - - Earth science 23
- - - Ecology 43
- - - Energy 29
- - - Experiments 30
- - - Geoengineering 0
- - - Mathematical methods 69
- - - Meta 9
- - - Methodology 16
- - - Natural resources 7
- - - Oceans 4
- - - Organizations 34
- - - People 6
- - - Publishing 4
- - - Reports 3
- - - Software 21
- - - Statistical methods 2
- - - Sustainability 4
- - - Things to do 2
- - - Visualisation 1
- General 41

## Comments

Maybe the simplest category without a terminal object is \( \textbf{2} := [ 1 \, 2 ] \) the discrete category of two objects.

Does \( \textbf{0} \) qualify? It has no morphisms (to any object) but it has no objects from which to draw a terminal-object so it has no terminal-object.

The category \( \textbf{1} \) has a terminal object but the category with one object and one morphism in addition to the identity-morphism does not have a terminal-object [uniqueness is violated].

`Maybe the simplest category without a terminal object is \\( \textbf{2} := [ 1 \, 2 ] \\) the discrete category of two objects. Does \\( \textbf{0} \\) qualify? It has no morphisms (to any object) but it has no objects from which to draw a terminal-object so it has no terminal-object. The category \\( \textbf{1} \\) has a terminal object but the category with one object and one morphism in addition to the identity-morphism does not have a terminal-object [uniqueness is violated].`