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The notion of independence in categories of algebraic structures, part I: Basic properties

Gabriel Srour
1988 Annals of Pure and Applied Logic  
The following are some examples. (a) In the category of fields F with field homomorphisms, we have the notion of independence.  ...  And also that we can de&~ (say, in a given class of structures) an independence relation with respect to a set of 'equations' in very much the same manner algebraic independence is in the class of gelds  ...  In Section 7, we introduce the notion of S-minimal amalgam and relate it to S&ninimal extensions.  ... 
doi:10.1016/0168-0072(88)90053-x fatcat:6iubugynsvhj5mpyatlwkt2mby

Strongly Minimal Steiner Systems II: Coordinatization and Quasigroups [article]

John T. Baldwin
2021 arXiv   pre-print
We note that a strongly minimal Steiner k-Steiner system (M,R) from (Baldwin-Paolini 2020) can be 'coordinatized' in the sense of (Gantner-Werner 1975) by a quasigroup if k is a prime-power.  ...  Nevertheless, by refining the construction, if k is a prime power there is a (2,k)-variety of quasigroups which is strongly minimal and definably coordinatizes a Steiner k-system.  ...  5 and ii) to employ a function µ to bound the number 0-primitive extensions of each finite structure so that closure in the geometry on the generic model for the resulting class of finite structures is  ... 
arXiv:2106.13704v1 fatcat:z7nu7rrysrgqran6ayxwyjmmie

Deformation theory of representations of prop(erad)s II

Sergei Merkulov, Bruno Vallette
2009 Journal für die Reine und Angewandte Mathematik  
To do so, we endow the category of prop(erad)s with a model category structure. We provide a complete study of models for prop(erad)s.  ...  Their underlying chain complex is endowed with a canonical Lie algebra up to homotopy structure in general and a Lie algebra structure only in the Koszul case.  ...  The first author expresses his thanks to the Max Planck Institute for Mathematics in Bonn and É cole Normale Supérieure in Paris for stimulating conditions during the work on this project.  ... 
doi:10.1515/crelle.2009.084 fatcat:urkjk2uenbg6ppzm3zoyqzo5we

Derived Algebraic Geometry II: Noncommutative Algebra [article]

Jacob Lurie
2007 arXiv   pre-print
We develop a general theory of algebras in a monoidal infinity category, which we use to (re)prove some basic results in the theory of associative ring spectra.  ...  We show that the infinity category of spectra admits an essentially unique monoidal structure (such that the tensor product preserves colimits in each variable), and thereby recover the classical smash-product  ...  We will also introduce the notion of an algebra object of a monoidal ∞-category C.  ... 
arXiv:math/0702299v5 fatcat:6tdcjvtqtjctvlqxahu7kvrtcu

Etale and crystalline companions, II [article]

Kiran S. Kedlaya
2022 arXiv   pre-print
In answer to a conjecture of Deligne, we establish that for any prime ℓ≠ p, an ℓ-adic Weil sheaf on X which is algebraic (or irreducible with finite determinant) admits a crystalline companion in the category  ...  of overconvergent F-isocrystals, for which the Frobenius characteristic polynomials agree at all closed points (with respect to some fixed identification of the algebraic closures of ℚ within fixed algebraic  ...  As for part (ii) of Theorem 0.1.1, by restricting to curves one sees that the coefficients in question are all algebraic, but one needs a uniformity argument over these curves to show that the extension  ... 
arXiv:2008.13053v3 fatcat:l5viqbz4frfjjfcpkcngrnhsba

Finite approximation properties of C^*-modules II [article]

Massoud Amini
2022 arXiv   pre-print
We introduce and study a notion of amenability for vector valued traces.  ...  We study quasidiagonality and local reflexivity for C^*-algebras which are C^*-module over another C^*-algebra with compatible actions.  ...  In section 3, we study a notion of quasidiagonality in the category of C * -modules and extend Voiculescu theorem (Theorem 3.6).  ... 
arXiv:2208.05655v1 fatcat:rstdaxmg5rdyvhoumgzr6a5tfm

Discrete derived categories II: The silting pairs CW complex and the stability manifold [article]

Nathan Broomhead, David Pauksztello, David Ploog
2015 arXiv   pre-print
In this article, we define the CW complex of silting pairs for a triangulated category and show that it is contractible in the case of discrete derived categories.  ...  We obtain that the space of stability conditions of discrete derived categories is contractible.  ...  The second author acknowledges the financial support  ... 
arXiv:1407.5944v2 fatcat:ensazlf5tnabbped22tbrjixyu

The geometry of Hrushovski constructions, II. The strongly minimal case [article]

David M. Evans, Marco S. Ferreira
2011 arXiv   pre-print
We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's flat strongly minimal structures and answer some questions from Hrushovski's original paper.  ...  But then Y ≤ Y ∪ {b ij } is a simply algebraic extension in Z 1 . As Y ≤ Z 1 is a minimally simply algebraic extension, this implies Y = {b i0 } ∪ s ij and Z 1 = {b i0 , b ij } ∪ s ij .  ...  We let µ be a function from the set of isomorphism types of minimally simply algebraic extensions in C 0 (L) to the non-negative integers.  ... 
arXiv:1103.3632v1 fatcat:imt66qkjt5h5bpwwha24izhhfm

On p-adic differential equations on semistable varieties II [article]

Valentina Di Proietto, Atsushi Shiho
2014 arXiv   pre-print
Given an open variety over a DVR with semistable reduction, the author constructed in that paper a fully faithful algebraization functor from the category of certain log overconvergent isocrystals on the  ...  special fiber to the category of modules with regular integrable connection on the generic fiber.  ...  (grant-in-aid) of the Japanese Society for the Promotion of Science (JSPS).  ... 
arXiv:1402.0720v1 fatcat:6trebuswjvc7tkuwa5qizgk6yi

Derived coisotropic structures II: stacks and quantization

Valerio Melani, Pavel Safronov
2018 Selecta Mathematica, New Series  
We extend results about n-shifted coisotropic structures from part I of this work to the setting of derived Artin stacks.  ...  We also compare non-degenerate shifted coisotropic structures and shifted Lagrangian structures and show that there is a natural equivalence between the two spaces in agreement with the classical result  ...  The work of P.S. was supported by the EPSRC grant EP/I033343/1.  ... 
doi:10.1007/s00029-018-0407-1 fatcat:xh7zcewndrfyxaf7nxspgzygja

Scaled-free objects II

Will Grilliette
2015 Annals of Functional Analysis  
This work creates two categories of "array-weighted sets" for the purposes of constructing universal matrix-normed spaces and algebras.  ...  Moreover, the universal matrix-normed algebra is used to prove the existence of a free product for matrix-normed algebras using algebraic methods.  ...  Proposition 4 . 8 . 48 If all x ∈ X are array-free in X, then N X = {0}. Theorem 4 . 9 ( 49 Array-free and finite sets, Part II).  ... 
doi:10.15352/afa/06-3-18 fatcat:oknu5s2usjg6pdyjeh532wlurm

On p-adic differential equations on semistable varieties II

Valentina Di Proietto, Atsushi Shiho
2014 Manuscripta mathematica  
category of log convergent isocrystals on X k with exponents in τ (Σ), which is the p-adic semistable version of the canonical logarithmic extension of Deligne, André-Baldassarri.  ...  Given an open variety over a DVR with semistable reduction, the author constructed in [10] a fully faithful algebraization functor from the category of certain log overconvergent isocrystals on the special  ...  (grant-in-aid) of the Japanese Society for the Promotion of Science (JSPS).  ... 
doi:10.1007/s00229-014-0691-9 fatcat:aqamddpn7fbtjj45lbi6i7cjpe

Sheaves on the alcoves and modular representations II [article]

Peter Fiebig, Martina Lanini
2020 arXiv   pre-print
We relate the category of sheaves on alcoves that was constructed in "Sheaves on the alcoves and modular representations I" to the representation theory of reductive algebraic groups.  ...  In particular, we show that its indecomposable projective objects encode the simple rational characters of a reductive algebraic group in all characteristics above the Coxeter number.  ...  As S is a full subcategory of the abelian category of sheaves of Z-modules on A, it inherits an exact structure, i.e. a notion of short exact sequences.  ... 
arXiv:1801.03958v3 fatcat:ckj5k363oje25fousue3an4yja

Strict algebraic models for rational parametrised spectra II [article]

Vincent Braunack-Mayer
2020 arXiv   pre-print
In this article, we extend Sullivan's PL de Rham theory to obtain simple algebraic models for the rational homotopy theory of parametrised spectra.  ...  While not full, the rational homotopy categories we consider contain a large class of parametrised spectra.  ...  For any cdga A in this class, the cohomology algebra H • (A) computes the cup product structure of H • (X; Q) and, conversely, the rational homotopy groups of X can be recovered from a minimal model of  ... 
arXiv:2011.06307v1 fatcat:pbcc5ehzpbaljfdjwnwq2u4l2y

Weak Hopf Algebras II: Representation theory, dimensions and the Markov trace [article]

G. Bohm, K. Szlachanyi
1999 arXiv   pre-print
In the special case of weak Kac algebras we show that I=δ is an integer.  ...  This category has isomorphic left dual and right dual objects which leads, as usual, to the notion of dimension function.  ...  for Part II.  ... 
arXiv:math/9906045v1 fatcat:6z5yxbkhengi3bn5w7bglcon6q
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