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Categorical constructions of free algebras, colimits, and completions of partial algebras. (English) Zbl 0403.18002


MSC:

18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
08A55 Partial algebras
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References:

[1] Adámek, J., Categorical automata theory and universal algebra (Czech), Thesis (1976), Charles University: Charles University Prague
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[10] F.E.J. Linton, Coequalizers in categories of algebras, Lecture Notes in Mathematics 80 (Springer- Verlag, Berlin) 75-90.; F.E.J. Linton, Coequalizers in categories of algebras, Lecture Notes in Mathematics 80 (Springer- Verlag, Berlin) 75-90. · Zbl 0181.02902
[11] MacLane, S., Categories for the Working Mathematician, GTM 6 (1971), Springer-Verlag: Springer-Verlag Berlin · Zbl 0232.18001
[12] Manes, E., Algebraic Theories, GTM 26 (1976), Springer-Verlag: Springer-Verlag Berlin · Zbl 0353.18007
[13] Reiterman, J., A left adjoint construction related to free triples, J. Pure Appl. Algebra, 10, 57-71 (1977) · Zbl 0385.18006
[14] Reiterman, J., A more categorical model of universal algebra, (Proc. FCT 77 (1977), Springer-Verlag: Springer-Verlag Berlin), 308-313, Lecture Notes in Computer Science · Zbl 0376.18005
[15] Reiterman, J., Categorical algebraic constructions (Czech), Thesis (1976), Charles University: Charles University Prague
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[17] Trnková, V.; Adámek, J.; Koubek, V.; Reiterman, J., Free algebras, input processes and free monads, Comment. Math. Univ. Carolinae, 16, 339-352 (1975) · Zbl 0308.18001
[18] R.O. Blackwell, Cocompleteness in a 2-category of algebras, Notices Amer. Math. Soc. 75T-A81.; R.O. Blackwell, Cocompleteness in a 2-category of algebras, Notices Amer. Math. Soc. 75T-A81.
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[20] Kelly, G. M., Quelques observations sur les demonstrations par recurrence transfinie en algebre categorique, Cahiers de Top. et Geom. Diff., 16, 259-263 (1975) · Zbl 0359.18006
[21] Kelly, G. M., Notes on the transfinite construction, Sydney Seminar (1975), preprint
[22] Schubert, H., Categories (1970), Springer-Verlag: Springer-Verlag Berlin, (English translation) · Zbl 0205.31904
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