On full embeddings of categories of algebras

Hedrlín, Z.; Pultr, Aleš

doi:10.1215/ijm/1256054991

Cited by 105 publications

(46 citation statements)

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“…In particular, Hedrlín and Pultr [35] showed in 1966 that every category of finite structures is "fully embeddable" in the category of finite graphs. (For a beautiful exposition, see [36].)…”

Section: Automorphism Group Vs Isomorphism Testingmentioning

confidence: 99%

On the automorphism groups of strongly regular graphs I

Babai

2014

Proceedings of the 5th Conference on Innovations in Theoretical Computer Science

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Section: Automorphism Group Vs Isomorphism Testingmentioning

confidence: 99%

On the automorphism groups of strongly regular graphs I

Babai

2014

Proceedings of the 5th Conference on Innovations in Theoretical Computer Science

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“…A quasivariety K is universal if every category of algebras of finite signature (or equivalently, as shown Pultr [92], Hedrlín and Pultr [60] and Vopěnka, Hedrlín, and Pultr [108], the category G of all directed graphs) is isomorphic to a full subcategory of K. If an embedding of G may be effected by a functor which assigns a finite algebraic system to each finite graph, then K is said to be finite-to-finite universal. Of particular interest for a universal quasivariety K is the fact that, for every monoid M , there exists a proper class of non-isomorphic algebraic systems belonging to K each of which has an endomorphism monoid isomorphic to M .…”

Section: Question 16 Is It True That If L(k) Satisfies No Nontrivialmentioning

confidence: 99%

Open questions related to the problem of Birkhoff and Maltsev

et al. 2004

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The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.Having whetted the reader's appetite in the preface to this special issue by claiming that much remains to be done in the theory of quasivarieties, we feel some responsibility to justify our claim. To do so, we will discuss the current status of the Birkhoff-Maltsev problem and consider open questions related to it.

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“…Let G a denote the full subcategory of non-trivial members of G where, for (G; E) in G a , if x ∈ G, (y, x) ∈ E for some y ∈ G. In Hedrlín and Pultr [6], it was shown that G a is finite-to-finite-universal. On the other hand, by Hedrlín and Pultr [5], there is a full and faithful functor F : G a −→ G u which we now specify.…”

Section: The Verification Of 11 and 12mentioning

confidence: 99%