英文:
initial and terminal object make the category unique?
问题
I've been reading Carli Masimo's book "Functional programming in Kotlin by tutorials," and there is a sentence not clear for me.
Not all categories have initial and terminal objects but, if they do, they are unique. In logic, the initial object has the name False and the terminal object True.
"unique" in this context means that if a category has initial and terminal objects, there is only one of each within that category. It refers to the uniqueness of these objects within the category itself.
英文:
I've been reading Carli Masimo book "Functional programming in Kotlin by tutorials" and there is a sentence not clear for me.
> Not all categories have initial and terminal objects but, if they do, they are
unique. In logic, the initial object has the name False and the terminal object
True.
what the unique means? the category or the initial-terminal? IMO, just the pair is unique, but it's likely the obvious by their name's meaning. and i think we can put more elements into sets of category so we can't say that the category unique. But i'm not sure because category theory is a mess with me. Thanks and appreciate any help.
答案1
得分: 2
你说得对。如果一个范畴有一个终端对象，那么终端对象是唯一的（在同构意义下）。同样，如果一个范畴有一个始端对象，那么始端对象也是唯一的（同样在同构意义下）。
英文:
You are right. If a category has a terminal object, the terminal object is unique (up to isomorphism). Similarly, if a category has an initial object, the initial object is unique (again up to isomorphism).
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