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Lifting results for categories of algebras
2002
Theoretical Computer Science
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A methodology is introduced that lifts adjoint pairs on categories with monads to categories whose objects are algebras for these monads. ...
In this paper, we present results that provide an abstract setting for the construction and interpretation of categories of algebras appearing in various semantic examples including those related to Scott ...
This paper focuses on lifting properties for categories of algebras. We brie y describe these categories. Deÿnition 2.3. Let (H; Á; ) be a monad on category C. ...
doi:10.1016/s0304-3975(00)00338-8
fatcat:yfvoefqskbdopkoiq6mlmotfwe
Monads in Semantics
1998
Electronical Notes in Theoretical Computer Science
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The abstract begins with some preliminary de nitions and examples, proceeds to categories of algebras and ends with some results and examples of the author using monadic lifting. ...
The treatment i s b y no means exhaustive but rather chooses examples and results that either illustrate the wide variety of uses of this abstract tool or which bearsome connection to other work presented ...
The abstract begins with some preliminary de nitions and examples, proceeds to categories of algebras, and ends with some results and examples of the author using monadic lifting. ...
doi:10.1016/s1571-0661(05)80241-5
fatcat:nx37qjq5bbfnvjddamvs3zwgdq
An algebraic model for rational naïve-commutative $G$-equivariant ring spectra for $\textrm{finite} \: G$
2019
Homology, Homotopy and Applications
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In this paper we let G be a finite group and we show that commutative algebras in the algebraic model for rational G-spectra model the rational naïve-commutative ring G-spectra. ...
Algebras over this operad are called naïve-commutative ring G-spectra. ...
The third author would like to thank Max Planck Institute for Mathematics in Bonn for hosting her during final stages of this project. ...
doi:10.4310/hha.2019.v21.n1.a4
fatcat:nl3fpdyrnzfy7pbcr7pcfw4jsu
An algebraic model for rational naive-commutative equivariant ring spectra
[article]
2017
arXiv
pre-print
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In this paper we let G be a finite group and we show that commutative algebras in the algebraic model for rational G-spectra model the rational naive-commutative ring G-spectra. ...
Algebras over this operad are called naive-commutative ring G-spectra. ...
The above results show that we have lifted model structures on each of the following categories. ...
arXiv:1708.09003v1
fatcat:z2wnluftjbb43noghf2pokgn6i
Algebraic weak factorisation systems I: Accessible AWFS
2016
Journal of Pure and Applied Algebra
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We provide a comprehensive treatment of the basic theory of AWFS---drawing on work of previous authors---and complete the theory with two main new results. ...
The first provides a characterisation of AWFS and their morphisms in terms of their double categories of left or right maps. ...
Of course, all these results have a dual form characterising coalgebras in terms of their liftings against algebras. 2.8. Double categories of algebras and coalgebras. ...
doi:10.1016/j.jpaa.2015.06.002
fatcat:s44jyzrbgrfqlkjtp2sbprtrii
Lifting to cluster-tilting objects in higher cluster categories
[article]
2008
arXiv
pre-print
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In this note, we consider the d-cluster-tilted algebras, the endomorphism algebras of d-cluster-tilting objects in d-cluster categories. ...
We show that a tilting module over such an algebra lifts to a d-cluster-tilting object in this d-cluster category. ...
The associated cluster category C H was introduced and studied in [3] , and also in [6] for algebras H of Dynkin type A n . ...
arXiv:0810.3360v2
fatcat:ay2jdrnpszfblmrnhgekxhsdui
On faithfulness of the lifting for Hopf algebras and fusion categories
2018
Algebra & Number Theory
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We use a version of Haboush's theorem over complete local Noetherian rings to prove faithfulness of the lifting for semisimple cosemisimple Hopf algebras and separable (braided, symmetric) fusion categories ...
certain classes of tensor functors between lifts of separable categories to characteristic zero can be reduced modulo p. ...
I am very grateful to Brian Conrad for useful discussions and help with writing Section 2, and to Davesh Maulik for comments on this section. I thank W. van der Kallen for Remark 2.2, ...
doi:10.2140/ant.2018.12.551
fatcat:bb3hqctkgree3el5cgjls6umvy
Lifting accessible model structures
[article]
2018
arXiv
pre-print
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We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted along either a left or a right adjoint. ...
A similar result was claimed in a paper of Hess-Kedziorek-Riehl-Shipley, but the proof given there was incorrect. ...
This result allows for a straightforward definition and a straightforward construction of left-and right-liftings for algebraic weak factorization systems. ...
arXiv:1802.09889v1
fatcat:qqwyuvpphndprkqipzs7hcw7ge
Right Bousfield Localization and Eilenberg-Moore Categories
[article]
2016
arXiv
pre-print
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En route, we provide conditions so that right Bousfield localization lifts to categories of algebras, so that right Bousfield localization preserves algebras over monads, and so that right Bousfield localization ...
We prove these approaches are equivalent, and we apply this equivalence to obtain several new results regarding right Bousfield localizations (some classical, some new) for spectra, spaces, equivariant ...
Thus, all results about right Bousfield localizations lifting to categories of algebras in Ch(k) yield analogous results in the category of simplicial k-modules. ...
arXiv:1609.03635v1
fatcat:x72ltjyz5bcz3epfefeqdftx7u
Bousfield Localization and Eilenberg-Moore Categories
[article]
2017
arXiv
pre-print
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We find conditions so that there is a model structure for local algebras, so that localization preserves algebras, and so that localization lifts to the level of algebras. ...
We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. ...
Acknowledgments We would like to thank the NSF EAPSI program for facilitating our collaboration, Macquarie University for hosting the second author during the summer of 2014 when this work began, and the ...
arXiv:1606.01537v2
fatcat:crtodfx5zfcsnh2t32kyetkhhm
On the construction of functorial factorizations for model categories
2013
Algebraic and Geometric Topology
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Our methods use "algebraic" characterizations of fibrations to produce factorizations that have the desired lifting properties in a completely categorical fashion. ...
Examples include the categories of (based) spaces, (based) G-spaces, and diagram spectra among others. ...
We would like to thank Richard Williamson for bringing this problem to our attention and Richard Garner, whose work inspired much of this paper. ...
doi:10.2140/agt.2013.13.1089
fatcat:f46eed3zpnb55hi4ykilwhkhem
Combining probabilistic and non-deterministic choice via weak distributive laws
2020
Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
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As a consequence, we retrieve the well-known convex powerset monad as a weak lifting of the powerset monad to the category of convex algebras. ...
From a category theory perspective, the problem stems from the absence of a distributive law of the powerset monad over the distribution monad. ...
category of algebras for the functor . ...
doi:10.1145/3373718.3394795
dblp:conf/lics/0003P20
fatcat:3mplbmedafg6lerggk4kssetku
Monoidal algebraic model structures
[article]
2013
arXiv
pre-print
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A main result is a simple criterion which shows that algebraic Quillen two-variable adjunctions correspond precisely to cell structures on the pushout-products of generating (trivial) cofibrations. ...
As a corollary, we discover that the familiar monoidal model structures on categories and simplicial sets admit this extra algebraic structure. ...
She continually appreciates the supportive environment provided by the algebraic topology and category theory seminar at the University of Chicago. ...
arXiv:1109.2883v3
fatcat:toxkz5xifjhkrldqu27kabsg2i
Monoidal algebraic model structures
2013
Journal of Pure and Applied Algebra
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A main result is a simple criterion which shows that algebraic Quillen two-variable adjunctions correspond precisely to cell structures on the pushout-products of generating (trivial) cofibrations. ...
As a corollary, we discover that the familiar monoidal model structures on categories and simplicial sets admit this extra algebraic structure. Proof. ...
She continually appreciates the supportive environment provided by the algebraic topology and category theory seminar at the University of Chicago. ...
doi:10.1016/j.jpaa.2012.09.029
fatcat:n3iblrldsbhcbpcm43v76ej4fa
Not all $\sigma$-complete Boolean algebras are quotients of complete Boolean algebras
1992
Proceedings of the American Mathematical Society
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In Shelah's model of no Borel lifting of the measure algebra we show that there is a a-complete Boolean algebra of cardinality 2m that is not a quotient of a complete Boolean algebra. ...
By Stone duality, there is a basically disconnected space of weight 2W that cannot be embedded into an extremally disconnected space. ...
Let us now recall the following result of Shelah. Proposition 2.2 (Shelah [8] ). There is a model in which there is no Borel lifting of the category algebra. ...
doi:10.1090/s0002-9939-1992-1137221-4
fatcat:n4fezmn6xzap5ok6y7jle2wl54
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