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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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[1] Adámek, J., Categorical automata theory and universal algebra (Czech), Thesis, (1976), Charles University Prague
[2] Adámek, J., Colimits of algebras revisited, Bull. austral. math. soc., 17, 433-450, (1977) · Zbl 0365.18007
[3] Adámek, J., Free algebras and automata realizations in the language of categories, Comment. math. univ. carolinae, 15, 589-602, (1974) · Zbl 0293.18006
[4] Adámek, J.; Koubek, V., Functorial algebras and automata, Kybernetika, 13, 245-260, (1977) · Zbl 0377.94065
[5] Arbib, M.; Manes, E., A Categorist’s view of automata and control, (), 62-78 · Zbl 0306.18002
[6] Arib, M.; Manes, E., Machines in a category: an expository introduction, SIAM review, 16, 163-192, (1974) · Zbl 0288.18005
[7] Barr, M., Coequalizers and free triples, Math. Z., 116, 307-322, (1970) · Zbl 0194.01701
[8] Koubek, V., Set functors, Comment. math. univ. carolinae, 12, 175-195, (1971) · Zbl 0217.06803
[9] Ku˚rková-Pohlová, V.; Koubek, V., When a generalized algebraic category is monadic, Comment. math. univ. carolinae, 15, 577-587, (1974) · Zbl 0294.18004
[10] 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 Berlin
[12] Manes, E., Algebraic theories, GTM 26, (1976), 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, (), 308-313, Lecture Notes in Computer Science
[15] Reiterman, J., Categorical algebraic constructions (Czech), Thesis, (1976), Charles University Prague
[16] Trnková, V., Some properties of set functors, Comment. math. univ. carolinae, 10, 323-352, (1969) · Zbl 0183.30401
[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.
[19] R.O. Blackwell, Some results on the existence of 2-monads, Notices Amer. Math. Soc. 737-18-9.
[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 Berlin, (English translation)
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