A universal property of the convolution monoidal structure
type: Item
instance of: scholarly article
title: A universal property of the convolution monoidal structure
zbMATH Open document ID: 0604.18004
DOI: 10.1016/0022-4049(86)90005-8
author: Geun Bin Im
author: Max Kelly
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: For a good base monoidal category V, suppose that A is a small monoidal V-category, that PA is the V-category \([A^{op},V]\) with its convolution monoidal structure [\textit{B. Day}, Lect. Notes Math. 137, 1-38 (1970; Zbl 0203.314)], and that C is a cocomplete monoidal V-category. The main result is that restriction along the Yoneda embedding is an equivalence between the category of cocontinuous monoidal functors from PA to C and the category of monoidal functors from A to C.
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 18A35
zbMATH DE Number: 3975173
zbMATH Keywords: closed category
zbMATH Keywords: enriched category
zbMATH Keywords: cocompletion
zbMATH Keywords: monoidal category
zbMATH Keywords: convolution
Wikidata QID: Q72421656
reviewed by: Ross H. Street
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90005-8
OpenAlex ID: W2015034783
cites work: Introduction to bicategories
cites work: On closed categories of functors
cites work: Construction of biclosed categories
cites work: Q5586461
cites work: Q5654206
cites work: Q5654207
cites work: Q4100657
cites work: Q4100671
cites work: Q3491793
description: scientific article; zbMATH DE number 3975173