side note: 36:51 isn't the relationship between Employees and Departments many-to-many? Is adherence to the relational model insignificant to David's category-theoretical representation?
32:00 mentions C->D (pre)composed to D->Set giving C->Set, mentioning a contravariant functor ... but these are Functors ... A contravariant functor would see morphisms compose this way ... so ... ? (processing)
@Paul McGee you're right that it is just normal composition of functors The contravariant functor here is Delta. It takes a morphism of schemas F:C->D to a morphism from the set of D-Instances to the set of C-Instances Delta_F: D-Inst -> C-Inst and it does so by taking an instance i : D->Set to F composed with i (F;i in Spivak's notation). We could rewrite it a little more functorially like this: Delta: Schema -> Set Delta(C) = C-Inst Delta(F): Delta(D) -> Delta(C) and then we'd have Delta(FG) = Delta(G)Delta(F)
2:15 starts
lol that guy in the front left cannot stop bouncin!! good for him
side note: 36:51 isn't the relationship between Employees and Departments many-to-many? Is adherence to the relational model insignificant to David's category-theoretical representation?
32:00 mentions C->D (pre)composed to D->Set giving C->Set, mentioning a contravariant functor ... but these are Functors ...
A contravariant functor would see morphisms compose this way ... so ... ? (processing)
Actually it just seems like normal composition ... c->d; d->set
@Paul McGee you're right that it is just normal composition of functors
The contravariant functor here is Delta. It takes a morphism of schemas F:C->D to a morphism from the set of D-Instances to the set of C-Instances
Delta_F: D-Inst -> C-Inst
and it does so by taking an instance i : D->Set to F composed with i (F;i in Spivak's notation). We could rewrite it a little more functorially like this:
Delta: Schema -> Set
Delta(C) = C-Inst
Delta(F): Delta(D) -> Delta(C)
and then we'd have Delta(FG) = Delta(G)Delta(F)
@@StewartMcGinnis nice. thank you
Should not the Grothendieck @34:30 construction include edges to nodes indicating the "able/type" to which they belong?
Is there a state monad and store comonad for databases? If so, how do they work?
Is David the son of Michael Spivak?