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12:00 AM
@skullpatrol who doesn't like hats?
 
12:16 AM
According to the vote count 17/76@robjohn
 
@skullpatrol I was the 76 :-)
 
@robjohn :D
 
12:40 AM
What do you call an object that represents the identity functor? I'm pretty sure these had a name I've heard. For instance hom(C[G],V)~V in the cat of G-Reps, and hom(G,X)~X in the cat of G-sets.
 
1:37 AM
Hi folks
 
@anon should there be a name? this only makes sense in categories enriched over themselves, which aren't so common
 
good point
never mind then
 
there probably is one for people who think about such things, but it's probably not common/well-known
 
or maybe replace "identity functor" with "forgetful functor"
for instance hom(Z,G)~F(G) in Grp, hom(Z[x],R)~F(R) in Ring, hom(k,V)~F(V) in Vect_k, hom(*,S)~F(S) in Top
 
well, forgetful functors are just things we call forgetful
 
1:44 AM
true
faithful functors to set
 
forgetting about names the objects themselves are interesting
objects in cats enriched over themselves that represent the identity
I don't have anything to say but I have a friend who could say some intelligent things if you post it
 
meh
 
not sure what the right questions are tho
 
I just want to be able to call the C[G] in hom_G(C[G],V)~V something cool because of this categorical property
suppose I could just call it The Source
 
with the caps, of course
is that really interesting? G-reps = C[G]-mod by defn and R is such a thing for all R-mod
 
1:51 AM
yes, I want to say the same thing about R in R-mod
 
if you must
 

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