Sketches
type: Item
instance of: scholarly article
title: Sketches
zbMATH Open document ID: 0943.18002
DOI: 10.1016/S0022-4049(98)00114-5
author: Yoshiki Kinoshita
author: Makoto Takeyama
author: John Power
published in: Journal of Pure and Applied Algebra
publication date: 2000-02-15T00:00:00Z
review text: Ehresmann's concept of sketch is very widely generalized here. The basis for it is an object \({\mathcal C}\) in some 3-dimensional categorical setting (such as locally finitely presentable 2-categories) and a monad \(T\) on \({\mathcal C}\). They take, as diagram types, arrows \(c,d:{\mathcal I}\to {\mathcal C}\) with a factorization of the unit of \(T\) into the composite of 2-cells \(j:c\to d\) and \(k:d\to Tc\). A sketch, relative to \(u:{\mathcal I}\to {\mathcal U}\) for this diagram type, consists of an arrow \(x:{\mathcal U}\to{\mathcal C}\) and a 2-cell \(p:d\to xu\). these sketches are modelled (strictly and strongly) in \(T\)-algebras \(a:{\mathcal U}\to{\mathcal C}\).
Mathematics Subject Classification ID: 18C05
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18C20
zbMATH DE Number: 1384152
zbMATH Keywords: model
zbMATH Keywords: theory
zbMATH Keywords: triple
zbMATH Keywords: sketch
zbMATH Keywords: locally finitely presentable
zbMATH Keywords: monad
reviewed by: Ross H. Street
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1384152