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A Fibrational Account of Local States

Kenji Maillard, Paul-Andre Mellies
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
This reconstruction is based on the guiding idea that an algebra of the indexed state monad should be defined as a section of a 2-categorical notion of fibration associated to the indexed state monad by  ...  Here, we study the particular case of the local state monad, which we would like to express as the result of combining together a family of global state monads parametrized by the number of available registers  ...  ACKNOWLEGMENTS The authors are grateful to Noam Zeilberger for nice and enlightning discussion during the preparation of this paper.  ... 
doi:10.1109/lics.2015.45 dblp:conf/lics/MaillardM15 fatcat:sibm5re2dvhhzmj3qefxg25npu

An Effective Characterization of Computability in Anonymous Networks [chapter]

Paolo Boldi, Sebastiano Vigna
2001 Lecture Notes in Computer Science  
., recursive) characterizations of the relations that can be computed on networks where all processors use the same algorithm, start from the same state, and know at least a bound on the network size.  ...  There is a very intuitive characterization of fibrations based on the concept of local isomorphism.  ...  Formally, a protocol P is given by a set X of local states, a distinguished subset F ⊆ X of final states, an input set ϒ, an input function in : ϒ → X , an output set , an output function 3 out : F → and  ... 
doi:10.1007/3-540-45414-4_3 fatcat:zn72fprvijcutbd3cex6uu7jmy

The singular set and aspects of global control dynamics [article]

Efthimios Kappos
2018 arXiv   pre-print
In this work, we define the singular set and examine some of its general properties. We then briefly examine its role in the global design of control dynamics.  ...  The global approach to control systems which we have been pursuing in other work favours the study of dynamics achievable through control.  ...  Control fibrations We now change gear and define a general control system on a smooth state space manifold M n , using the notion of a fibration.  ... 
arXiv:1812.04850v1 fatcat:gq7levdxc5fb3cge6lu2ahvhhi

Page 3905 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
While a more com- plete account should appear shortly in the Annals of Mathematics, the present work is the first published account of these ideas.  ...  For a space that is not semi-locally simply connected, the second part of the proof exhibits a family of loops indexed by the sets of nat- ural numbers.  ... 

Page 1104 of Mathematical Reviews Vol. 42, Issue 5 [page]

1971 Mathematical Reviews  
To complete the calculation of K,(F') one must therefore account for ker(A).  ...  No. 35 (1968), 157-222; MR 39 #5575] states that the Hilbert symbol above is universal for continuous symbols on F, with values in locally compact abelian groups.  ... 

Page 1187 of Mathematical Reviews Vol. 38, Issue 6 [page]

1969 Mathematical Reviews  
B are locally flat and tame p-spheres (p21), then f is topologically a (p+1)-fold suspension of a fibering S"~?  ...  By its construction, however, the Bott map fails to take into account much of the non-stable homotopy theory of U(n). We propose to prove the fol- lowing result. Theorem: There is a map 6,”: £?  ... 

Homotopy theoretic models of identity types

2008 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
It is shown that a form of intensional type theory is valid in any Quillen model category, generalizing the Hofmann-Streicher groupoid model of Martin-Loef type theory.  ...  This paper presents a novel connection between homotopical algebra and mathematical logic.  ...  We give special thanks to Ieke Moerdijk, for suggesting this research topic, and to Nicola Gambino and Thomas Streicher for many useful discussions and detailed comments on a draft of this paper.  ... 
doi:10.1017/s0305004108001783 fatcat:3j43ofr4dbhldmsrukj6z6zymq

A fibrational framework for possible-world semantics of Algol-like languages

C. Hermida, R.D. Tennent
2007 Theoretical Computer Science  
) where V is a set (of values for "new" local variables) and m is a monic function (to impose constraints on the local states). • The identity on W is 1, id W , !  ...  [10] provides a fairly comprehensive account of fibrations in categorical logic and type theory.  ... 
doi:10.1016/j.tcs.2006.12.025 fatcat:jmdg3rmqljcvzkaklwdp53c7p4

Fibrations of highly singular map germs [article]

Maico F. Ribeiro, Raimundo N. Araújo dos Santos, Mihai Tibăr
2019 arXiv   pre-print
We define local fibration structures for real map germs with strictly positive dimensional discriminant: a local fibration structure over the complement of the discriminant, and a complete local fibration  ...  We provide new classes of map germs endowed with such local fibration structures.  ...  In this new setting the following problems have to be taken into account so that the fibration problem can be well posed: (a) the local fibration must be independent of the small enough neighbourhood data  ... 
arXiv:1711.07544v6 fatcat:kypvr7ds7ja7zlqgiryo6blly4

When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion

Florent Baume, Mirjam Cvetič, Craig Lawrie, Ling Lin
2018 Journal of High Energy Physics  
To this end we consider complex structure deformations of elliptic fibrations with a Mordell--Weil group of rank one and identify the conditions under which the generating section becomes torsional.  ...  The subsolution with gauge group SU(2)/Z2 x SU(2), for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian  ...  Note that the uncharged (Cartan) states of the codimension one deformation modes are accounted for in the h 2,1 ( Ŷ ) uncharged hypermultiplets.  ... 
doi:10.1007/jhep03(2018)069 fatcat:k4myi2spmvcilpra5kwm5lnpk4

Page 257 of Mathematical Reviews Vol. , Issue 91A [page]

1991 Mathematical Reviews  
of the fiber of the fibration p, together with certain finiteness conditions, implies nilpotence of the components of the mapping space. (3) Fiberwise equivariant localization of Y leads to localization  ...  Precisely, given a G-fibration p: Y — B of G-connected based G-spaces, and a G- map u: X — B, he considers the space of equivariant liftings of u to Y.  ... 


J. Miller, M. Palmer
2014 Quarterly Journal of Mathematics  
The purpose of this note is to clarify some details in McDuff and Segal's proof of the group-completion theorem and to generalize both this and the homology fibration criterion of McDuff to homology with  ...  This will be used in forthcoming work to identify the limiting homology of "oriented" configuration spaces, which doubly cover the classical configuration spaces of distinct unordered points in a manifold  ...  In Remark 2 of [MS75] , McDuff and Segal stated a version of the groupcompletion theorem for twisted coefficient systems.  ... 
doi:10.1093/qmath/hau030 fatcat:dv7tfl5ygfev5aztlfidodw6qq

The SYZ conjecture via homological mirror symmetry [article]

Dori Bejleri
2017 arXiv   pre-print
The goal of these notes is to give a motivated introduction to the Strominger-Yau-Zaslow (SYZ) conjecture from the point of view of homological mirror symmetry.  ...  These are expository notes based on a talk given at the Superschool on derived categories and D-branes at University of Alberta in July of 2016.  ...  Indeed a theorem of Arnol'd and Liouville states that the smooth fibers of any Lagrangian fibration of a symplectic manifold are tori [Arn89, Section 49].  ... 
arXiv:1710.05894v1 fatcat:cqbqdth3wvf33i6j7gwct3fhcq

Integral Brown-Gitler Spectra

Fred R. Cohen, Donald M. Davis, Paul G. Goerss, Mark E. Mahowald
1988 Proceedings of the American Mathematical Society  
A Thorn spectrum model for integral Brown-Gitler spectra is established and shown to have a multiplicative property. This clarifies certain aspects of an earlier application to splitting bo A bo.  ...  The map of total spaces induces an isomorphism in mod p homology, and, since 7Pn+i is ¿¿Fp»-local, this map is an ¿¿Fp*-localization, and so there is an equivalence of fibrations extending the induction  ...  Localizing Lemma 2.1 yields a map Mpn(dlpn)p -> Jpn_! ~ Sp1 xAn-l, and, since H1(MPn(dIpn)p; Zp) = 0, the map is of the form * x h. Let Y denote the mapping cone of h.  ... 
doi:10.2307/2047129 fatcat:kgllfvm4xneybmqfoohynupltm

Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy

Daisuke Tarama
2012 Central European Journal of Mathematics  
This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces.  ...  There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.  ...  He also thanks Professor Isao Naruki for a lot of useful discussions.  ... 
doi:10.2478/s11533-012-0050-6 fatcat:qsuvecmfjfc2dexlkd3h2tm334
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