Index
df, see also fiber diagram
Fun(I,C), see also diagram category
Funb(1L,C),
see also bounded diagram
Ftm^ (L,C), see also bounded diagram,relatively
to map
/-bounded, see also bounded diagram,relatively
to map
/-cofibrant, see also cofibrant,relative
/-cofibration, see also cofibration,relative
/-non-degenerate, see also non-degenerate,relatively
to map
GrjH^ see also Grothendieck construction
G T K H , see also Grothendieck construction
id-bounded, see also bounded diagram,absolutely
red(f), see also reduction of a map
A, see also simplicial category
A[n, k], see also standard simplex,horn of
A[n], see also standard simplex
f li, see also over category,of a functor
14,2, see also over category
K, L, N, see also simplex category
K x N , see also simplex category,product
5A[n], see also standard simplex,boundary
of
etale space, 64, 69
absolutely bounded, see also bounded dia-
gram , absolutely
absolutely cofibrant, see also cofibrant,absolutely
additivity
of the colimit, 23
of the homotopy colimit, 36
of the etale space, 64
basic space, 66
bounded diagram, 26, 72
absolutely, 39
over a Grothendieck construction, 58
over a horn, 28
over a product, 54
over a sphere, 28
over a standard simplex, 27
relatively to map, 38
strongly, 26
Bousfield-Kan approximation, 29, 36, 56, 73
Bousfield-Kan model approximation, 61
Brown's lemma, 12, 34, 49
category
over an object, see also over category
under an object, see also under category
co-Grothendieck construction, 73
cofibrant, 6
absolutely, 44
bounded diagram, 30, 54, 59
over a sphere, 31
constant bounded diagram, 31
relatively to a map, 44
replacement, 7
of a diagram, 38
cofibration, 6
absolute, 44
acyclic, 6
of bounded diagrams, 30
over a Grothendieck construction, 59
over a product, 54
relative, 44
cofinal functor, 24, 36, 70, 83
colimit, 5, 14, 83
compatible family, 57, 85
cone
over a category, 50
over a space, 49
over a standard simplex, 50
coproduct, 10
cylinder object, 8
derived functor
left, 12
right, 71
total left, 12, 18
total right, 71
diagram
almost cubical, 27
constant, 31
indexed by a space, 22
diagram category, 5, 14
factorization
functorial, 36, 38
factorization axiom, 7, 33
fiber diagram, 24, 28, 75
fibrant, 6
replacement, 8
fibration, 6
89
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