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Topoi over graphs. (English) Zbl 0546.18004

A. Burroni [ibid. 22, 249-265 (1981; Zbl 0497.18004)] and subsequently E. J.Dubuc and G. M. Kelly [J. Algebra 81, 420- 433 (1983; Zbl 0516.18009)] have shown that the forgetful functor from the category of toposes and (strictly) logical functors to the category of directed graphs is monadic. The goal of the present paper is to give an explicit presentation of the former over the latter by operations and equations; there are 21 operations and 67 equations.
Reviewer: P.T.Johnstone

MSC:

18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
18B25 Topoi
18A10 Graphs, diagram schemes, precategories
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References:

[1] 1 A. Burroni , Algèbres graphiques , Cahiers Top. Géom. Dif. XXII - 2 ( 1981 ), 249 . Numdam | MR 649074 | Zbl 0497.18004 · Zbl 0497.18004
[2] 2 A. Freyd , Aspects of topoi , Bull. Austral. Math. Soc. 7 ( 1972 ), 1 - 76 . MR 396714 | Zbl 0252.18001 · Zbl 0252.18001 · doi:10.1017/S0004972700044828
[3] 3 J. Lambek , Toposes are monadic over categories , to appear. MR 682953 | Zbl 0497.18007 · Zbl 0497.18007
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