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En-Algebras in m-Categories
En-Algebras in m-Categories
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105146
- ISBN
- 9798265408174
- DDC
- 510
- 저자명
- Liu, Yu.
- 서명/저자
- En-Algebras in m-Categories
- 발행사항
- [Sl] : Harvard University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 96 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-05, Section: A.
- 주기사항
- Advisor: Hopkins, Mike.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2025.
- 초록/해제
- 요약The study of En-algebras in higher categories has attracted growing interests, both from various categorification programs in mathematics as well as the study of higher dimensional topological orders in physics. However, the complexity of these structures increases rapidly with the category level. In this thesis, we prove a connectivity bound for maps of ∞-operads of the form Ak1 ⊗ · · · ⊗ Akn → En, and as a consequence, give an inductive way to construct En-algebras in m-categories. To prove this result, we first develop a theory of arity restricted unital ∞-operads. Given k ≥ 1, we define unital k-restricted ∞-operads, which are variants of ∞-operads which have only (≤ k)-arity morphisms, as complete Segal presheaves on closed k-dendroidal trees, which are closed trees built from corollas with valences ≤ k. Furthermore, we prove that the restriction functors from unital ∞-operads to unital k-restricted ∞-operads admit fully faithful left and right adjoints by showing that the left and right Kan extensions preserve complete Segal objects. Varying k, the left and right adjoints give a filtration and a co-filtration for any unital ∞-operad by k-restricted ∞-operads, generalizing the Ak filtration for E1. Second, We prove a version of Eckmann-Hilton argument that takes into account both connectivity and arity of ∞-operads. Along the way, we prove a technical Blakers-Massey type statement for algebras of coherent ∞-operads.
- 일반주제명
- Mathematics
- 일반주제명
- Mathematics education
- 키워드
- Category theory
- 키워드
- Operands
- 기타저자
- Harvard University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-05A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798265408174
■035 ▼a(MiAaPQ)AAI32241236
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aLiu, Yu.
■24510▼aEn-Algebras in m-Categories
■260 ▼a[Sl]▼bHarvard University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a96 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-05, Section: A.
■500 ▼aAdvisor: Hopkins, Mike.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2025.
■520 ▼aThe study of En-algebras in higher categories has attracted growing interests, both from various categorification programs in mathematics as well as the study of higher dimensional topological orders in physics. However, the complexity of these structures increases rapidly with the category level. In this thesis, we prove a connectivity bound for maps of ∞-operads of the form Ak1 ⊗ · · · ⊗ Akn → En, and as a consequence, give an inductive way to construct En-algebras in m-categories. To prove this result, we first develop a theory of arity restricted unital ∞-operads. Given k ≥ 1, we define unital k-restricted ∞-operads, which are variants of ∞-operads which have only (≤ k)-arity morphisms, as complete Segal presheaves on closed k-dendroidal trees, which are closed trees built from corollas with valences ≤ k. Furthermore, we prove that the restriction functors from unital ∞-operads to unital k-restricted ∞-operads admit fully faithful left and right adjoints by showing that the left and right Kan extensions preserve complete Segal objects. Varying k, the left and right adjoints give a filtration and a co-filtration for any unital ∞-operad by k-restricted ∞-operads, generalizing the Ak filtration for E1. Second, We prove a version of Eckmann-Hilton argument that takes into account both connectivity and arity of ∞-operads. Along the way, we prove a technical Blakers-Massey type statement for algebras of coherent ∞-operads.
■590 ▼aSchool code: 0084.
■650 4▼aMathematics
■650 4▼aMathematics education
■653 ▼aAlgebraic topology
■653 ▼aCategory theory
■653 ▼aOperands
■690 ▼a0405
■690 ▼a0280
■71020▼aHarvard University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-05A.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359614▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
