J.R.B. Cockett. Introduction to distributive categories. Math. Struct. in Comp. Science, 3:277-307, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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On Impartiality - Benson (Correct)
....a coproduct decomposition, a family of monics fX k Xg which are the coproduct injections. Each such family is called a cover. A thorough discussion of covers may be found in [Sri91] The collection of all such coproduct decomposition covers provides a Grothendieck topology on F , denoted by d, [Coc90]. From [Man92] choosing one coproduct injection Y . X fixes the complement of Y with respect to X;Y 0 , so that Y ....
J. R. B. Cockett, Introduction to Distributive Categories, Macquarie University Computing Report No. 90--0052C, April 1990.
Stone Duality Between Queries And Data - Benson (1996) (2 citations) (Correct)
....with arbitrary limit specifications but only coproduct specifications in the colimit specification part of the sketch. A category of Diers categories, rich in arrows, is cartesian closed, 6] Johnstone s logic, 17] was designed to be the logic of Diers categories. Related topics appear in [12, 13]. From the definition of a Diers category, define the queries on a Diers category of data A as B = ConnF ilt (A; Sets) the category of all functors from A to Sets preserving connected limits and filtered colimits. Since coproducts commute with connected limits, one obtains the ....
J. R. B. Cockett, Introduction to distributive categories, Math. Struc. Comput. Sci. 3(1993), 277-307.
The Extensive Completion Of A Distributive Category - Cockett, Lack (2001) (1 citation) Self-citation (Cockett) (Correct)
....But there are many other examples which are not toposes, such as the category Top of topological spaces and continuous maps, the category Hty of topological spaces and homotopy classes of maps, the poset P(X) of subsets of a set X, or the opposite of the category of commutative rings. The papers [3, 6] contain an introduction to distributive categories; see also the book [16] A category E with finite coproducts is said to be extensive if the functors E AE B # E (A B) sending a pair (f : X # A, g : Y # B) to f g : X Y # A B are equivalences of categories for all objects A ....
....category can fail to be distributive by failing to have finite products, but this is in fact the only possible problem: every extensive category with finite products is distributive. For a proof of this, and a general introduction to extensive categories, see once again either of the papers [3, 6]. Thus among the distributive categories are the extensive categories with products. Our main result is to construct for each distributive category D an extensive category with products D ex equipped with a functor D # D ex which preserves finite products and finite coproducts and is the ....
J.R.B. Cockett, Introduction to distributive categories, Math. Structures Comput. Sci. 3:277--307, 1993.
! and ? -- Storage as tensorial strength - R. F. Blute, J. R.B. Cockett.. (1996) Self-citation (Cockett) (Correct)
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Cockett, J.R.B. (1993) Introduction to distributive categories. Math. Struct. in Comp. Science 3, 277--308.
Logical Construction of Final Coalgebras - Santocanale (2003) (Correct)
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J.R.B. Cockett. Introduction to distributive categories. Math. Struct. in Comp. Science, 3:277-307, 1993.
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