/sci/ - Science & Math

Thinkin' about math n shit. Is Lurie's book on higher topos theory a good way to introduce oneself to the world of topos homotopy?

A nice little result I came up with maybe a week ago is that if [math]\mathscr{E}[/math] is a category in which terminal objects are initial (for example an abelian category), then all its objects are initial if [math]\mathscr{E}[/math] is a topos. This follows from the fact that, in a topos, any arrow whose codomain is initial is an isomorphism. This, naturally, affects the spoopy skeletons of such categories, and thus there is only one equivalence class of abelian toposes.

On the other hand, in a well-powered abelian category satisfying a distributivity condition, there could be (I'm making this up while writing) a topos of disjoint subobjects for any object. This idea came to me from the fact that a topos satisfying certain conditions is a Heyting algebra, and so a frame. Anyone here know any conditioms for this to be true?

>>9024047
I'm quite sure this thing is equivalent to the AC, sorry.

>>9024948
Reading Logicomix and Logik, språk och filosofi by Georg Henrik von Wright. I try to spend a few hours every day thinking about mathsy stuff, even if I'm not studying.