scholarly journals Some categorical aspects of the inverse limits in ditopological context

2018 ◽  
Vol 19 (1) ◽  
pp. 101
Author(s):  
Filiz Yildiz
Keyword(s):  
Compatibility Condition ◽  
Natural Transformation ◽  
Inverse Limits ◽  
Infinite Products ◽  
Inverse Systems ◽  
Finite Products

<p>This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if<strong>PDitop</strong>, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category <strong>Inv<sub>ifPDitop</sub></strong> consisting of the inverse systems constructed by the objects and morphisms of if<strong>PDitop</strong>, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in if<strong>PDitop</strong> and the ditopological infinite products are characterized by the finite products via inverse limits.</p>

Profinite Modules

1973 ◽  
Vol 16 (3) ◽  
pp. 405-415
Author(s):  
Gerard Elie Cohen
Keyword(s):  
Finite Group ◽  
General Theory ◽  
Finite Length ◽  
Finite Groups ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Point Of View ◽  
Inverse Limits ◽  
Profinite Groups ◽  
Inverse Systems

An inverse limit of finite groups has been called in the literature a pro-finite group and we have extensive studies of profinite groups from the cohomological point of view by J. P. Serre. The general theory of non-abelian modules has not yet been developed and therefore we consider a generalization of profinite abelian groups. We study inverse systems of discrete finite length R-modules. Profinite modules are inverse limits of discrete finite length R-modules with the inverse limit topology.

scholarly journals Tripleableness of pro-c-groups

1976 ◽  
Vol 21 (3) ◽  
pp. 299-309 ◽  
Author(s):  
Lim Chong-Keang
Keyword(s):  
Algebraic Number ◽  
Full Subcategory ◽  
Forgetful Functor ◽  
Galois Groups ◽  
Inverse Limits ◽  
Discrete Groups ◽  
Profinite Groups ◽  
Finite Products

Let C be a nontrivial full subcategory of the category F of finite discrete groups and continuous homomorphisms, closed under subobjects, quotient and finite products. We consider the category PC of pro-C-groups and continuous homomorphisms (i.e. inverse limits of C-groups) which forms a variety in category PF of profinite groups and continuous homomorphisms. The study of pro-Cgroups is motivated by their occurrence as Galois groups of filed extensions in algebraic number thory (see Serre (1965)). The purpose of this paper is to study the tripleableness of the forgetful functors from PC to various underlying categories. It is also shown that PC is equivalent to the category of algebras of the theory of the forgetful functor from C to S (the category of sets and mappings).

scholarly journals Coherence for monoidal endofunctors

2010 ◽  
Vol 20 (4) ◽  
pp. 523-543 ◽  
Author(s):  
KOSTA DOŠEN ◽  
ZORAN PETRIĆ
Keyword(s):  
Monoidal Category ◽  
Natural Transformation ◽  
Monoidal Categories ◽  
Monoidal Structure ◽  
Natural Transformations ◽  
Finite Products ◽  
Relational Graphs

The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, that is, endofunctors of a monoidal category that preserve the monoidal structure up to a natural transformation that need not be an isomorphism. These results are proved first in the absence of symmetry in the monoidal structure, and then with this symmetry. In the later parts of the paper, the coherence results are extended to monoidal endofunctors in monoidal categories that have diagonal or codiagonal natural transformations, or where the monoidal structure is given by finite products or coproducts. Monoidal endofunctors are interesting because they stand behind monoidal monads and comonads, for which coherence will be proved in a sequel to this paper.

Elementary epimorphisms

2005 ◽  
Vol 70 (2) ◽  
pp. 473-487 ◽  
Author(s):  
Philipp Rothmaler
Keyword(s):  
Inverse Limits ◽  
Elementary Chain ◽  
Flat Modules ◽  
Inverse Systems

AbstractThe concept of elementary epimorphism is introduced. Inverse systems of such maps are considered, and a dual of the elementary chain lemma is found (Cor. 4.2). The same is done for pure epimorphisms (Cor. 4.3 and 4.4). Finally, this is applied to certain inverse limits of flat modules (Thm. 6.4) and certain inverse limits of absolutely pure modules (Cor. 6.3).

Big and large continua in inverse limits of inverse systems over directed graphs

2020 ◽  
Vol 274 ◽  
pp. 107119
Author(s):  
Iztok Banič ◽  
Matevž Črepnjak ◽  
Peter Goričan ◽  
Teja Kac ◽  
Matej Merhar ◽  
...  
Keyword(s):  
Directed Graphs ◽  
Inverse Limits ◽  
Inverse Systems

scholarly journals Inverse limits of Macaulay's inverse systems

2019 ◽  
Vol 525 ◽  
pp. 341-358
Author(s):  
Mathias Schulze ◽  
Laura Tozzo
Keyword(s):  
Inverse Limits ◽  
Inverse Systems

scholarly journals Coherence for monoidal monads and comonads

2010 ◽  
Vol 20 (4) ◽  
pp. 545-561 ◽  
Author(s):  
KOSTA DOŠEN ◽  
ZORAN PETRIĆ
Keyword(s):  
Modal Logic ◽  
Monoidal Category ◽  
Natural Transformation ◽  
Monoidal Structure ◽  
Monoidal Functor ◽  
Finite Products ◽  
Relational Graphs ◽  
Modal Logic S4

The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, that is, monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor (this means that it preserves the monoidal structure up to a natural transformation that need not be an isomorphism). These results are proved first in the absence of symmetry in the monoidal structure, and then with this symmetry. The monoidal structure is also allowed to be given with finite products or finite coproducts. Monoidal comonads with finite products axiomatise a plausible notion of equality of deductions in a fragment of the modal logic S4.

Productly linearly independent sequences

2015 ◽  
Vol 52 (3) ◽  
pp. 350-370
Author(s):  
Jaroslav Hančl ◽  
Katarína Korčeková ◽  
Lukáš Novotný
Keyword(s):  
Rational Numbers ◽  
Infinite Products ◽  
Linearly Independent ◽  
New Concepts ◽  
Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

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