Enriched yoneda lemma

Vladimir Hinich

Enriched yoneda lemma

Department of Mathematics

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

Abstract

We present a version of the enriched Yoneda lemma for conventional (not ∞-) cate-gories. We do not require the base monoidal category M to be closed or symmetric monoidal. In the case M has colimits and the monoidal structure in M preserves colimits in each argument, we prove that the Yoneda embedding A → P_M(A) is a universal functor from A to a category with colimits, left-tensored over M.

Original language	English
Article number	29
Pages (from-to)	833-838
Number of pages	6
Journal	Theory and Applications of Categories
Volume	31
State	Published - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© Vladimir Hinich, 2016.

Keywords

Enriched categories
Left-tensored categories
Yoneda embedding

ASJC Scopus subject areas

Mathematics (miscellaneous)

Cite this

@article{39ce66082a294957bfedbb7702d31dd6,

title = "Enriched yoneda lemma",

abstract = "We present a version of the enriched Yoneda lemma for conventional (not ∞-) cate-gories. We do not require the base monoidal category M to be closed or symmetric monoidal. In the case M has colimits and the monoidal structure in M preserves colimits in each argument, we prove that the Yoneda embedding A → PM(A) is a universal functor from A to a category with colimits, left-tensored over M.",

keywords = "Enriched categories, Left-tensored categories, Yoneda embedding",

author = "Vladimir Hinich",

note = "Publisher Copyright: {\textcopyright} Vladimir Hinich, 2016.",

year = "2016",

month = sep,

day = "1",

language = "English",

volume = "31",

pages = "833--838",

journal = "Theory and Applications of Categories",

issn = "1201-561X",

publisher = "Mount Allison University",

}

TY - JOUR

T1 - Enriched yoneda lemma

AU - Hinich, Vladimir

N1 - Publisher Copyright: © Vladimir Hinich, 2016.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We present a version of the enriched Yoneda lemma for conventional (not ∞-) cate-gories. We do not require the base monoidal category M to be closed or symmetric monoidal. In the case M has colimits and the monoidal structure in M preserves colimits in each argument, we prove that the Yoneda embedding A → PM(A) is a universal functor from A to a category with colimits, left-tensored over M.

AB - We present a version of the enriched Yoneda lemma for conventional (not ∞-) cate-gories. We do not require the base monoidal category M to be closed or symmetric monoidal. In the case M has colimits and the monoidal structure in M preserves colimits in each argument, we prove that the Yoneda embedding A → PM(A) is a universal functor from A to a category with colimits, left-tensored over M.

KW - Enriched categories

KW - Left-tensored categories

KW - Yoneda embedding

UR - http://www.scopus.com/inward/record.url?scp=84987784700&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84987784700

SN - 1201-561X

VL - 31

SP - 833

EP - 838

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

M1 - 29

ER -

Enriched yoneda lemma

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this