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One more categorical model of universal algebra. (English) Zbl 0363.18007


MSC:

18B20 Categories of machines, automata
68Q45 Formal languages and automata
18B15 Embedding theorems, universal categories
18C05 Equational categories
18B10 Categories of spans/cospans, relations, or partial maps
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
08B20 Free algebras
08Axx Algebraic structures
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References:

[1] Adámek, J.: Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolinae15, 589-602 (1974) · Zbl 0293.18006
[2] Adámek, J.: Categorical automata theory and universal algebra [in Czech.] Thesis, Charles University Prague, Prague 1975
[3] Barr, M.: Coequalizers and free triples. Math. Z.116, 307-322 (1970) · Zbl 0197.29204
[4] Hales, A.W.: On the non-existence of free complete Boolean algebras. Fund. Math.54, 45-66 (1964) · Zbl 0119.26003
[5] Linton, F.E.J.: Some aspects of equational categories. In: Proceedings of the conference on categorical algebra (La Jolla, 1965), pp. 84-94. Berlin-Heidelberg-New York: Springer 1966
[6] Manes, E.G.: Algebraic theories. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0353.18007
[7] Reiterman, J.: A left adjoint construction related to free triples. J. Pure Appl. Algebra10, 57-72 (1977) · Zbl 0385.18006
[8] Reiterman, J.: A more categorical model of universal algebra. In: Fundamentals of computation theory. Proceedings of the International FCT-Conference (Pozna?-Kárnik, 1977), pp. 308-313. Lecture Notes in Computer Science56. Berlin-Heidelberg-New York: Springer 1977
[9] Reiterman, J.: Categorical algebraic constructions [in Czech.] Thesis, Charles University Prague, Prague, 1976
[10] Trnková, V., Adámek, J., Koubek, V., Reiterman, J.: Free algebras, input processes and free monads. Comment. Math. Univ. Carolinae16, 339-352 (1975) · Zbl 0308.18001
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