COLIMITS IN ENRICHED ∞-CATEGORIES AND DAY CONVOLUTION

Vladimir Hinich

COLIMITS IN ENRICHED ∞-CATEGORIES AND DAY CONVOLUTION

Vladimir Hinich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let M be a monoidal ∞-category with colimits. In this paper we study colimits of M-functors A → B where B is left-tensored over M and A is an M-enriched category. We prove that the enriched Yoneda embedding Y: A → P_M(A) yields a universal M-functor. In case when A has a certain monoidal structure, the category of enriched presheaves P_M(A) inherits the same monoidal structure and the enriched Yoneda embedding acquires the structure of universal monoidal M-functor.

Original language	English
Pages (from-to)	365-422
Number of pages	58
Journal	Theory and Applications of Categories
Volume	39
Issue number	12
State	Published - 2023

Bibliographical note

Publisher Copyright:
© Vladimir Hinich, 2023.

Keywords

Day convolution
enriched categories
left-tensored categories

ASJC Scopus subject areas

Mathematics (miscellaneous)

Cite this

@article{35d20ddcf27c4bb19d9ccffc915cbab0,

title = "COLIMITS IN ENRICHED ∞-CATEGORIES AND DAY CONVOLUTION",

abstract = "Let M be a monoidal ∞-category with colimits. In this paper we study colimits of M-functors A → B where B is left-tensored over M and A is an M-enriched category. We prove that the enriched Yoneda embedding Y: A → PM(A) yields a universal M-functor. In case when A has a certain monoidal structure, the category of enriched presheaves PM(A) inherits the same monoidal structure and the enriched Yoneda embedding acquires the structure of universal monoidal M-functor.",

keywords = "Day convolution, enriched categories, left-tensored categories",

author = "Vladimir Hinich",

note = "Publisher Copyright: {\textcopyright} Vladimir Hinich, 2023.",

year = "2023",

language = "English",

volume = "39",

pages = "365--422",

journal = "Theory and Applications of Categories",

issn = "1201-561X",

publisher = "Mount Allison University",

number = "12",

}

TY - JOUR

T1 - COLIMITS IN ENRICHED ∞-CATEGORIES AND DAY CONVOLUTION

AU - Hinich, Vladimir

N1 - Publisher Copyright: © Vladimir Hinich, 2023.

PY - 2023

Y1 - 2023

N2 - Let M be a monoidal ∞-category with colimits. In this paper we study colimits of M-functors A → B where B is left-tensored over M and A is an M-enriched category. We prove that the enriched Yoneda embedding Y: A → PM(A) yields a universal M-functor. In case when A has a certain monoidal structure, the category of enriched presheaves PM(A) inherits the same monoidal structure and the enriched Yoneda embedding acquires the structure of universal monoidal M-functor.

AB - Let M be a monoidal ∞-category with colimits. In this paper we study colimits of M-functors A → B where B is left-tensored over M and A is an M-enriched category. We prove that the enriched Yoneda embedding Y: A → PM(A) yields a universal M-functor. In case when A has a certain monoidal structure, the category of enriched presheaves PM(A) inherits the same monoidal structure and the enriched Yoneda embedding acquires the structure of universal monoidal M-functor.

KW - Day convolution

KW - enriched categories

KW - left-tensored categories

UR - https://www.scopus.com/pages/publications/85152700313

M3 - Article

AN - SCOPUS:85152700313

SN - 1201-561X

VL - 39

SP - 365

EP - 422

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

IS - 12

ER -

COLIMITS IN ENRICHED ∞-CATEGORIES AND DAY CONVOLUTION

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this