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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Algebras and Modules in Monoidal Model Categories
 Proc. London Math. Soc
, 1998
"... In recent years the theory of structured ring spectra (formerly known as A #  and E # ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect t ..."
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Cited by 243 (34 self)
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In recent years the theory of structured ring spectra (formerly known as A #  and E # ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect
Stabilization of model categories
, 1998
"... monoidal structure which is compatible with the model structure. Given a monoidal model category, we consider the homotopy theory of modules over a given monoid and the homotopy theory of monoids. We make minimal assumptions on our model categories; our results therefore are more general, yet weaker ..."
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Cited by 335 (12 self)
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monoidal structure which is compatible with the model structure. Given a monoidal model category, we consider the homotopy theory of modules over a given monoid and the homotopy theory of monoids. We make minimal assumptions on our model categories; our results therefore are more general, yet
Existence of minimal models for varieties of log general type
 J. AMER. MATH. SOC
, 2008
"... We prove that the canonical ring of a smooth projective variety is finitely generated. ..."
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Cited by 386 (34 self)
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We prove that the canonical ring of a smooth projective variety is finitely generated.
Adjunctions
, 1993
"... ing from the particulars, the situation above is described as follows. ffl There are two categories A and B . [In the above example A = Set and B = Mon .] ffl There are two functors F : A ! B and G: B ! A . [Above Ff = Seq f and Gg = g for arrows f and g . For objects the functors act as follows: ..."
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an adjunction. It is rather easy to verify the given adjunction SeqAdj from the explicit definitions we have given for Mon; tip; join; Seq ; ...
Cohomology of Monoids in Monoidal Categories
 In &quot;Operads: Proceedings of renaissance conferences.&quot; Contemp. Math. 202, AMS
, 1997
"... this article we show that these structures are still susceptible to cohomological investigation, by developing the theory in the absence of the symmetry condition. Later we shall assume that the monoidal structure is left distributive over coproducts and the category is an abelian category; this is ..."
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Cited by 8 (2 self)
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this article we show that these structures are still susceptible to cohomological investigation, by developing the theory in the absence of the symmetry condition. Later we shall assume that the monoidal structure is left distributive over coproducts and the category is an abelian category
Local Reasoning about Programs that Alter Data Structures
, 2001
"... We describe an extension of Hoare's logic for reasoning about programs that alter data structures. We consider a lowlevel storage model based on a heap with associated lookup, update, allocation and deallocation operations, and unrestricted address arithmetic. The assertion language is ba ..."
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Cited by 324 (29 self)
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We describe an extension of Hoare's logic for reasoning about programs that alter data structures. We consider a lowlevel storage model based on a heap with associated lookup, update, allocation and deallocation operations, and unrestricted address arithmetic. The assertion language is based on a possible worlds model of the logic of bunched implications, and includes spatial conjunction and implication connectives alongside those of classical logic. Heap operations are axiomatized using what we call the "small axioms", each of which mentions only those cells accessed by a particular command. Through these and a number of examples we show that the formalism supports local reasoning: A speci cation and proof can concentrate on only those cells in memory that a program accesses. This paper builds on earlier work by Burstall, Reynolds, Ishtiaq and O'Hearn on reasoning about data structures.
in monoidal categories
, 1995
"... We consider the theory of operads and their algebras in enriched category theory. We introduce the notion of simplicial A~cgraph and show that some important constructions of homotopy coherent category theory lead by a natural way to the use of such objects as the appropriate homotopy coherent coun ..."
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We consider the theory of operads and their algebras in enriched category theory. We introduce the notion of simplicial A~cgraph and show that some important constructions of homotopy coherent category theory lead by a natural way to the use of such objects as the appropriate homotopy coherent counterparts of the categories. @ 1998 Elsevier Science B.V. 1991 Math. Subj. Class.. " 18D20, 18D35, 18{330 Let A be a small simplicial category, and let F, G: A ~ K be two simplicial functors to a simplicial category K. Then we can consider, as the simplicial set of coherent natural transformations from F to G, the coherent end [8, 10, 12] (see Definition 6.2): Coh(F, G) =.fA K(F():) , G(2)).
A GALOIS THEORY FOR MONOIDS
, 2014
"... We show that the adjunction between monoids and groups obtained via the Grothendieck group construction is admissible, relatively to surjective homomorphisms, in the sense of categorical Galois theory. The central extensions with respect to this Galois structure turn out to be the socalled special ..."
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We show that the adjunction between monoids and groups obtained via the Grothendieck group construction is admissible, relatively to surjective homomorphisms, in the sense of categorical Galois theory. The central extensions with respect to this Galois structure turn out to be the so
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