Terminal and initial objects 2

Full proof that terminal objects are unique up to unique isomorphism, and some examples of categories without terminal objects

Category:

Howto & Style

Tags:

• category
• terminal
• object
• isomorphism
• universal

[TheCatsters]

Yes - there is a unique morphism T->T. g o f and the identity are both morphisms T->T so they must be equal.

[gggeeesssuuu]

You guys rock!!

Thanks for posting all these videos

[GoAwayStupidAI]

I don't quite follow why the morphism g : T' -> T composed with f : T -> T', g o f, must equal the identity morphism of T. Is this implied by the uniqueness of the morphisms to the terminal object T?

Assuming there was a morphism h : T -> T that was not the identity morphism of T then there is not a unique morphism from T to T. This contradicts the fact that T is a terminal object therefor any morphism from T -> T must be the identity. Something like that?