/sci/ - Science & Math

>>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.