122 INDEX
extension condition, 56
extension of an S-module map, 93
extension of an n-deformation, 22
fiber of a morphism, 16
filler of a horn, 56
first order deformation, 15
flat L∞-algebra, 100
flat deformation, 12
formal deformation, 14, 15
formality, 84
free R-module, 2
free operad, 89
gap of deformation, 21
gauge equivalence, 66
gauge group, 11, 49
generators of an operad, 90
geometrically rigid algebra, 23
Gerstenhaber bracket, 25, 110
Gerstenhaber-Hochschild algebra, 26, 110
global deformation, 12
graded B-bimodule, 33
graded associative algebra, 33
graded commutativity, 57
graded Jacobi identity, 26
graded Lie algebra, 26
grading convention for A∞-algebras, 35
Grassmann algebra, 57, 69, 114
Hausdorff-Campbell formula, 45
Hochschild cochains, 19, 109
Hochschild cohomology, 19, 109
Hochschild complex, 19
Hochschild differential, 19, 110
homogeneous functor, 54
homotopic 0-simplexes, 56
homotopy associativity, 35
homotopy equivalence, 66
horn, 56
ideal in an operad, 90
induced L∞-structure, 76
infinitesimal deformation, 15
infinitesimally rigid algebra, 23
initial operad, 91
intrinsic L∞-algebra, 109
intrinsic bracket, 109
isomorphism of A∞-algebras, 53
isomorphism of L∞-algebras, 77
Jacobiator, 29
Kan fibration, 73
Kan simplicial set, 56
Koszul sign, 69
Leibniz rule, 92
length grading, 90
Lie admissible algebras, 27
Lie bialgebra, 120
lower central series, 72
master equation, 28
Maurer-Cartan element, 28
Maurer-Cartan equation, 28
Maurer-Cartan moduli space, 49, 60
minimal L∞-algebra, 78
minimal model, 80, 94
minimal operad, 93
minimal resolution, 94
miniversal deformation, 16
module, 2
monad cohomology, 100
morphism of P-algebras, 87
morphism of S-modules, 89
morphism of A∞-algebras, 53
morphism of L∞-algebras, 75
morphism of associative algebras, 10
morphism of dg-operads, 93
morphism of operads, 85
nilpotent L∞-algebra, 72
nilpotent dg-Lie algebra, 62
operad, 85
operad unit, 85, 88
operadic cochains, 99
operadic cohomology, 99
opetopic sequence, 38
Poisson algebra, 81
Poisson bivector, 83
Poisson manifold, 82
polyvector fields, 83
pre-Lie algebra, 26
presentation of an operad, 90
PROP, 120
push-forward, 11
quadratic differential, 42
quadratic coderivation, 42
quadratic Koszul operad, 111
rectification, 81
relations of an operad, 90
resolution of a dg-operad, 93
restriction of an (n + 1)-deformation, 22
rigid algebra, 23
ring, 1
sh Lie algebra, 70
Shouten-Nijenhuis bracket, 83
sh associative algebra, 34
sign convention for A∞-algebras, 35
sign convention for L∞-algebras, 70
simplicial L∞-Maurer-Cartan space, 72
simplicial algebra, 58
simplicial Maurer-Cartan space, 60
simplicial object, 55
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