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 343
- Applied Category Theory Exercises 149
- Applied Category Theory Discussion Groups 48
- Applied Category Theory Formula Examples 15
- Chat 475
- Azimuth Code Project 107
- News and Information 145
- Azimuth Blog 148
- Azimuth Forum 29
- Azimuth Project 190
- - Strategy 109
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 708
- - Latest Changes 700
- - - 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 20
- - - Statistical methods 2
- - - Sustainability 4
- - - Things to do 2
- - - Visualisation 1
- General 38

Options

## Comments

A terminal object in

Cone\((X,Y)\) is a pair of morphisms \(X\xleftarrow[]{\pi_1}X\times Y\xrightarrow[]{\pi_2}Y\) such that for every pair of morphisms \(X\xleftarrow[]{f}C\xrightarrow[]{g}Y\), there is a unique morphism \((f,g):C\to X\times Y\) such that \(\pi_1\circ(f,g)=f\) and \(\pi_2\circ(f,g)=g\). This is exactly the same as the definition of the product of \(X\) and \(Y\) (cf. Definition 3.81).`A terminal object in **Cone**\\((X,Y)\\) is a pair of morphisms \\(X\xleftarrow[]{\pi_1}X\times Y\xrightarrow[]{\pi_2}Y\\) such that for every pair of morphisms \\(X\xleftarrow[]{f}C\xrightarrow[]{g}Y\\), there is a unique morphism \\((f,g):C\to X\times Y\\) such that \\(\pi_1\circ(f,g)=f\\) and \\(\pi_2\circ(f,g)=g\\). This is exactly the same as the definition of the product of \\(X\\) and \\(Y\\) (cf. Definition 3.81).`