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/sci/ - Science & Math

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6204706 No.6204706 [Reply] [Original]

Given a category (not necessarily a bi-category or 2-category) does Hom(1,X) always have the structure of a category?

>> No.6204708

no

>> No.6204710

yea shit

>> No.6204711

define 1
define X

>> No.6204717

>>6204711
If you were the kinda person who could help - it would be obvious.

1 is the terminal object, and X is any object of the category

>> No.6204844

>>6204717
>terminal object
what the hell does this computer word doing with mathematics

>> No.6204862

>>6204844
category theory is a little above your head, go play in the IQ thread

>> No.6204864
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6204864

>>6204844

>>>/b/

>> No.6204876
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6204876

>cats

>> No.6204879
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6204879

>>6204862
>>6204864

>> No.6204885

>>6204717
if you were the kinda person that could understand category theory - it would be obvious

>> No.6204921

Yes, but in what sense?
I assume you want something more than the discrete category.

>> No.6205028

Never mind worked it out myself

>> No.6205233

>>6205028
Care to explain?
You never answered my above question.
The structure you are looking for involves a map from f to g that looks like 1 -> a -> 1 -> g, right?

>> No.6206292
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6206292

>>6205233
I was looking for the wrong thing. I thought the right way to get it was to impose that Hom(1,X) was a category, but in fact what I wanted was the following category...

Let C(X) be the full subcategory containing X and its endomorphisms let i:C(X) -> C be its embedding in C.

The comma category 1/i is what I was looking for. It's objects are the global elements x:1 -> X and it's morphisms are g:x -> y such that gx=y in C.