Symmetric Monoidal Categories for Operads - Index of

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18.2 Shifted Functors and Pushouts 275 of the previous latching morphism λ : Ln(Y/X) → Y ⊗n−1 with i : X → Y . This observation follows from an immediate interchange of colimits. Because of this observation, we also refer to the morphism λ : Ln(Y/X) → Tn(Y/X)asann-fold pushout-product of i : X → Y . 18.2.8 Iterated Pushout-Products and Functor Decomposition. The symmetric group Σn acts naturally (on the right) on Tn(Y/X)andLn(Y/X). Moreover the latching morphism λ : Ln(Y/X) → Tn(Y/X) is equivariant. For a Σ∗-object N, weset TnN[Y/X]=N(n+ · )⊗ΣnTn(Y/X)andLnN[Y/X]=N(n+ · )⊗ΣnLn(Y/X). Note that TnN[Y/X] (respectively, LnN[Y/X]) inherits the structure of a right R-module if N has this structure. By definition, we have TnN[Y/X]=N(n + · ) ⊗Σn Y ⊗n and the morphism of lemma 18.2.5 has an obvious factorization � p+q=n N(n + · ) ⊗Σp×Σq X q
276 18 Shifted Modules over Operads and Functors pushout based on LnN[X/Y ], use that the morphism � p+q=n Σn ⊗Σp×Σq q
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Lecture Notes in Mathematics 1967 E
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Benoit Fresse UFR de Mathématiques
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vi Preface Γ -object, which occur
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viii Contents 9 Algebras in Right M
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Introduction Main Ideas and Objecti
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Introduction 3 The category of Σ
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Introduction 5 the bar module BC to
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Introduction 7 modules over envelop
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Introduction 9 to a P-algebra in ri
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Introduction 11 DerP(A, E). There i
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Introduction 13 In both contexts (m
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22 1 Symmetric Monoidal Categories
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36 2 Symmetric Objects and Functors
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54 3 Operads and Algebras in Symmet
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Chapter 5 Definitions and Basic Con
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5.1 The Functor Associated to a Rig
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Chapter 6 Tensor Products Introduct
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6.1 The Symmetric Monoidal Category
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6.3 On Enriched Category Structures
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Chapter 7 Universal Constructions o
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7.2 Extension and Restriction of St
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122 8 Adjunction and Embedding Prop
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140 10 Miscellaneous Examples 10.1.
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142 10 Miscellaneous Examples Let
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144 10 Miscellaneous Examples Proof
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146 10 Miscellaneous Examples In th
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Chapter 11 Symmetric Monoidal Model
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11.1 Recollections: The Language of
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11.2 Examples of Model Categories i
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11.3 Symmetric Monoidal Model Categ
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11.4 The Model Category of Σ∗-Ob
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11.4 The Model Category of Σ∗-Ob
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11.5 The Pushout-Product Property f
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11.6 Symmetric Monoidal Categories
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Chapter 12 The Homotopy of Algebras
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12.1 Semi-Model Categories 187 Simi
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12.1 Semi-Model Categories 189 The
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12.1 Semi-Model Categories 191 Say
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12.2 The Semi-Model Category of Ope
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12.2 The Semi-Model Category of Ope
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12.3 The Semi-Model Categories of A
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12.3 The Semi-Model Categories of A
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12.5 The Homotopy of Extension and
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Chapter 13 The (Co)homology of Alge
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13.1 The Construction 205 13.1.2 Pr
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13.1 The Construction 207 associate
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13.2 Universal Coefficient Spectral
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