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Involutive category theory / Donald Yau.
Math/Physics/Astronomy Library QA3 .L28 no.2279
Available
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2384 2385-2386,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Yau, Donald Y. (Donald Ying), 1977- author.
- Series:
- Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2279.
- Lecture Notes in Mathematics, 0075-8434 ; 2279
- Language:
- English
- Subjects (All):
- Categories (Mathematics).
- Operads.
- Physical Description:
- xii, 243 pages ; 24 cm.
- Place of Publication:
- Cham, Switzerland : Springer, [2020]
- Contents:
- Intro
- Preface
- Contents
- 1 Category Theory
- 1.1 Basic Concepts of Category Theory
- 1.2 Monoidal Categories
- 1.3 Monads
- 1.4 Colimits in Cat
- 1.5 Exercises and Notes
- 1.5.1 Notes
- 2 Involutive Categories
- 2.1 Definition and Examples
- 2.2 Involutive Functors
- 2.3 Involutive Natural Transformations and Adjunctions
- 2.4 Involutive Equivalences
- 2.5 Involutive Objects
- 2.6 Lifting Structures to Involutive Objects
- 2.7 Exercises and Notes
- 3 Coherence of Involutive Categories
- 3.1 Free Strict Involutive Categories
- 3.2 Free Involutive Categories
- 3.3 Strictification of Free Involutive Categories
- 3.4 Involutive Categories as Monadic Algebras
- 3.5 Presentability of Involutive Categories
- 3.6 Right Adjoint of the Forgetful Functor
- 3.7 Exercises
- 4 Involutive Monoidal Categories
- 4.1 Definitions and Examples
- 4.2 Rigidity of Involutive Monoidal Categories
- 4.3 Involutive Monoidal Functors
- 4.4 Involutive Monoidal Category of Involutive Objects
- 4.5 Involutive Monoids
- 4.6 Involutive Commutative Monoids
- 4.7 Reversing Involutive Monoids
- 4.8 Involutive Monads
- 4.9 Exercises and Notes
- 5 Coherence of Involutive Monoidal Categories
- 5.1 Free Involutive Monoidal Categories
- 5.2 Free Involutive Strict Monoidal Categories
- 5.3 Commutativity of Formal Diagrams
- 5.4 Strictification of Involutive Monoidal Categories
- 5.5 Free Involutive Monoidal Categories of Involutive Categories
- 5.6 Free Involutive Strict Monoidal Categories of InvolutiveCategories
- 5.7 Exercises and Notes
- 6 Coherence of Involutive Symmetric Monoidal Categories
- 6.1 Free Involutive Symmetric Monoidal Categories
- 6.2 Free Involutive Strict Symmetric Monoidal Categories
- 6.3 Commutativity of Formal Diagrams
- 6.4 Strictification of Involutive Symmetric Monoidal Categories
- 6.5 Free Involutive Symmetric Monoidal Categories of Involutive Categories
- 6.6 Free Involutive Strict Symmetric Monoidal Categories of Involutive Categories
- 6.7 Exercises
- 7 Categorical Gelfand-Naimark-Segal Construction
- 7.1 Monoid Inner Product Objects
- 7.2 Correspondence Between States and Inner Products
- 7.3 Proofs of Technical Lemmas
- 7.4 Exercises and Notes
- 8 Involutive Operads
- 8.1 Operads
- 8.2 Algebras
- 8.3 Involutive Operads as Involutive Monoids
- 8.4 Involutive Monads from Involutive Operads
- 8.5 Involutive Algebras of Involutive Operads
- 8.6 Change of Involutive Symmetric Monoidal Categories
- 8.7 AQFT Involutive Operad
- 8.8 Exercises and Notes
- Symbol Definition List
- Bibliography
- Index
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 9783030612023
- 3030612023
- OCLC:
- 1230406533
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