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ON COLIMITS OVER ARBITRARY POSETS

Part of: General theory of categories and functors Ordered sets

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

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 1 , January 2016 , pp. 219 - 228
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

REFERENCES

1.Assem, I., Castonguay, D., Marcos, E. N. and Trepode, S., Quotients of incidence algebras and the Euler characteristic, Commun. Algebra 35 (4) (2007), 1075–1086.CrossRefGoogle Scholar
2.Bourbaki, N., Éléments de mathématique. Théorie des ensembles (Paris, Hermann, 1970).Google Scholar
3.Bucur, I. and Deleanu, A., Introduction to the theory of categories and functors (Wiley Interscience, N.Y., 1968).Google Scholar
4.Gibbons, J., Towards a colimit-based semantics for visual programming, in Coordination models and languages. Proceedings of the 5th International Conference, COORDINATION 2002, York, GB, April 8–11 (F, Arbab. et al., Editors) Lect. Notes Comput. Sci., vol. 2315 (Springer, Berlin, 2002), 166–173.Google Scholar
5.Cheng, C. and Mitchell, B., DCC posets of cohomological dimension one, J. Pure Appl. Algebra 13 (1978), 125–137.CrossRefGoogle Scholar
6.Dräxler, P., Completely separating algebras, J. Algebra 165 (2) (1994), 550–565.CrossRefGoogle Scholar
7.Duffus, D., Rival, I., Retracts of partially ordered sets, J. Austral. Math. Soc. (Series A) 27 (1979), 495–506.CrossRefGoogle Scholar
8.Exel, R., Noncommutative Cartan subalgebras of C*-algebras, New York J. Math. 17 (2011), 331–382.Google Scholar
9.Goguen, J. A., Categorical foundations for general systems theory, in Advances in cybernetics and system research (Transcripta Books, London, 1973), 121–130.Google Scholar
10.Goguen, J. A., A categorical manifesto, Math. Struct. Comput. Sci. 1 (1) (1991), 49–67.CrossRefGoogle Scholar
11.Hardie, K. A. and Witbooi, P. J., Crown multiplications and a higher order Hopf construction, Topology Appl. 154 (10) (2007), 2073–2080.CrossRefGoogle Scholar
12.Eilenberg, S. and Steenrod, N. E., Foundations of algebraic topology (Princeton University Press, Princeton, New Jersey, 1952).CrossRefGoogle Scholar
13.Oriat, C., Detecting equivalence of modular specifications with categorical diagrams, Theor. Comput. Sci. 247 (1–2) (2000), 141–190.CrossRefGoogle Scholar
14.Smith, D. R., Composition by colimit and formal software development, in Algebra, meaning and computation. Essays dedicated to Joseph A. Goguen on the occasion of his 65th birthday (Futatsugi, K.et al., Editors) Lecture Notes in Computer Science, vol. 4060 (Springer, Berlin, 2006), 317–332.CrossRefGoogle Scholar