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A Fibrational Account of Local States

2015
*
2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
*

This reconstruction is based on the guiding idea that an algebra

doi:10.1109/lics.2015.45
dblp:conf/lics/MaillardM15
fatcat:sibm5re2dvhhzmj3qefxg25npu
*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. ...##
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An Effective Characterization of Computability in Anonymous Networks
[chapter]

2001
*
Lecture Notes in Computer Science
*

., recursive) characterizations

doi:10.1007/3-540-45414-4_3
fatcat:zn72fprvijcutbd3cex6uu7jmy
*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 ...##
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The singular set and aspects of global control dynamics
[article]

2018
*
arXiv
*
pre-print

In this work, we define the singular set and examine some

arXiv:1812.04850v1
fatcat:gq7levdxc5fb3cge6lu2ahvhhi
*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*. ...##
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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

doi:10.1017/s0305004108001783
fatcat:3j43ofr4dbhldmsrukj6z6zymq
*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. ...##
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A fibrational framework for possible-world semantics of Algol-like languages

2007
*
Theoretical Computer Science
*

) where V is

doi:10.1016/j.tcs.2006.12.025
fatcat:jmdg3rmqljcvzkaklwdp53c7p4
*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. ...##
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Fibrations of highly singular map germs
[article]

2019
*
arXiv
*
pre-print

We define

arXiv:1711.07544v6
fatcat:kypvr7ds7ja7zlqgiryo6blly4
*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 ...##
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When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion

2018
*
Journal of High Energy Physics
*

To this end we consider complex structure deformations

doi:10.1007/jhep03(2018)069
fatcat:k4myi2spmvcilpra5kwm5lnpk4
*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. ...##
###
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. ...

##
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A TWISTED HOMOLOGY FIBRATION CRITERION AND THE TWISTED GROUP-COMPLETION THEOREM

2014
*
Quarterly Journal of Mathematics
*

The purpose

doi:10.1093/qmath/hau030
fatcat:dv7tfl5ygfev5aztlfidodw6qq
*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. ...##
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The SYZ conjecture via homological mirror symmetry
[article]

2017
*
arXiv
*
pre-print

The goal

arXiv:1710.05894v1
fatcat:cqbqdth3wvf33i6j7gwct3fhcq
*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]. ...##
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Integral Brown-Gitler Spectra

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. ...

##
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Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy

2012
*
Central European Journal of Mathematics
*

This note deals with Lagrangian

doi:10.2478/s11533-012-0050-6
fatcat:qsuvecmfjfc2dexlkd3h2tm334
*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. ...
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