scratch

§ Kan Extensions: Key Idea

created 2022-04-03
  • The key insight is to notice that when we map from C→EC \to EC→E via KKK, then the K(x)K(x)K(x) object that we get whose comma we form with K↓KxK \downarrow KxK↓Kx also has an arrow Kx→KxKx \to KxKx→Kx via the identity arrow. Thus we can think of K↓KxK \downarrow KxK↓Kx as looking like ( -> Kx) -> Kx. So it's really the Kxin the -> Kx that controls the situation.
❦
Newer ৪ Blog ৪ Older