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ON COLIMITS OVER ARBITRARY POSETS

Part of: Ordered sets General theory of categories and functors

Published online by Cambridge University Press:  22 July 2015

M. DOKUCHAEV  and
B. NOVIKOV
M. DOKUCHAEV
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, SP, Brasil e-mail: dokucha@ime.usp.br
B. NOVIKOV
Affiliation:
Kharkov National University, Svobody sq., 4 61077, Kharkov, Ukraine e-mail: boris.v.novikov@univer.kharkov.ua
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Abstract

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We characterize those partially ordered sets I for which the canonical maps Mi → colim Mj into colimits of abstract sets are always injective, provided that the transition maps are injective. We also obtain some consequences for colimits of vector spaces.

MSC classification

Primary: 18A30: Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
Secondary: 06A06: Partial order, general
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 1 , January 2016 , pp. 219 - 228
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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