VERS UNE STRUCTURE DE CATÉGORIE DE - IMJ-PRG

n
n
2
n > 2
n
nCat
n
2
n > 2
n
W
n
2
2Cat
W

Cat
Cat
Ho(Cat )Hot = Ho( b ∆)
Cat
Cat
Cat
Ho(Cat )Hot
(∞,1)
Cat
K
K
Cat
Cat
nCat 1≤n≤ ∞
n n
n
n=∞
n≥1nCat nCat

nCat
n
n= 1
nCat
n
n
n n
n n
Θn
nCat
n
n
n
n
2Cat
2
2
2Cat
Cat
Cat 2Cat
2
Ho(2 Cat )Hot
nCat
n= 2
2

nCat
CUC
F
C
C
U Ex2U
Ex
Sd (F Sd2, Ex2U)
C=Cat U
C=nCat U=Nnn
nCat cnNn
0E0//E
cnN
E N(E)//NncnN(E)
n= 2
2Cat
(∞,1) Ho(2 Cat ) (∞,1) Hot
Cat
2Cat
i:E0//E
02
c2N(i) : c2N(E0)//c2N(E)
r
H ri c2N(E) 2
H: ∆1×c2N(E)//c2N(E)
2
0

nCat
c2N(i)i
2
n > 20
0nCat n > 2
n n > 2
( ) n n
n
nCat
0< m < n m Cat //nCat
n
nCat
n
W
W