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