Homotopical Quantum Field Theory

"This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using a new coend definition of the Boardman-Vogt construction for a colored operad. All of their homotopy coherent structures are explained in details, along with a comparison between the two approaches at the operad level. With chapters on basic category theory, trees, and operads, this book is self-contained and is accessible to graduate students."--

12.2 Configured Categories to Orthogonal Categories

Intro -- Contents -- Preface -- 1. Introduction -- 1.1 Algebraic Quantum Field Theory -- 1.2 Homotopy Algebraic Quantum Field Theory -- 1.3 Homotopy Prefactorization Algebra -- 1.4 Comparison -- 1.5 Organization -- Audience -- 2. Category Theory -- 2.1 Basics of Categories -- 2.2 Examples of Categories -- 2.3 Limits and Colimits -- 2.4 Adjoint Functors -- 2.5 Symmetric Monoidal Categories -- 2.6 Monoids -- 2.7 Monads -- 2.8 Localization -- 3. Trees -- 3.1 Graphs -- 3.2 Tree Substitution -- 3.3 Grafting -- 4. Colored Operads -- 4.1 Operads as Monoids

4.2 Operads in Terms of Generating Operations -- 4.3 Operads in Terms of Partial Compositions -- 4.4 Operads in Terms of Trees -- 4.5 Algebras over Operads -- 5. Constructions on Operads -- 5.1 Change-of-Operad Adjunctions -- 5.2 Model Category Structures -- 5.2.1 Model Categories -- 5.2.2 Model Structure on Algebra Categories -- 5.3 Changing the Base Categories -- 5.4 Localizations of Operads -- 5.5 Algebras over Localized Operads -- 6. Boardman-Vogt Construction of Operads -- 6.1 Overview -- 6.2 Commutative Segments -- 6.3 Coend Definition of the BV Construction -- 6.4 Augmentation

6.5 Homotopy Morita Equivalence -- 6.6 Filtration …