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Added paragraphs, corrected some English
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edit approved Jul 16 at 16:39
jeq
edit approved Jul 16 at 16:39
jeq
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I will try to say something about hypergroups  ( moremore generally about the hyperstructures) and hopefully it be useful and can answer to the the questions: How is a canonical hypergroup to be thought of as canonical? Are noncanonical hypergroups important? Is there a category theoretic way to see these hyperstructures as natural? The

The canonical hypergroups aa subclass(or precisely a subcategory of hypergroups) in fact thet are a subclass of polygroup  ( oror non-commutative hypergroup). One of importance of canonical hypergroup is to constitute Krasner hyperrings, in this hypestructure we deal with to a canonical hypergroup (H, +) with a binary product ., which satisfies the axioms similar a ring. Another importance of canonical is its application to other subjects in mathematics and physics etc. as example above mentioned by Gjergji Zaimi. Another, application is to study the categories of hyperstructures(based on various morphisms, especially multivaled homomorphisms of commutative hypergroups) which thesethese morphisms constitute an structures such as Abelian category (not exactly that) for.

For more study of categories of syperstructureshyperstructures see the following References: [1]

[1] R. Ameri, A. Borzooei and M. Hamidi, On categorical connections of hyperrings and rings via the fundamental relation, Int. J. Algebraic Hyperstructures Appl., 1(1) (2014), 108–121. [2]

[2] Ameri, R., On categories of hypergroups and hypermodules, Italian Journal of Pure and Applied Mathematics, vol. 6 (2003), 121-132. [3]

[3] A CONNECTION BETWEEN CATEGORIES OF OF (FUZZY) MULTIALGEBRAS AND (FUZZY) ALGEBRAS, italianItalian journal of pure and applied mathematics,208, (2010) 201-208.

I will try to say something about hypergroups( more generally about the hyperstructures) and hopefully it be useful and can answer to the the questions: How is a canonical hypergroup to be thought of as canonical? Are noncanonical hypergroups important? Is there a category theoretic way to see these hyperstructures as natural? The canonical hypergroups a subclass(or precisely a subcategory of hypergroups) in fact thet are a subclass of polygroup( or non-commutative hypergroup). One of importance of canonical hypergroup is to constitute Krasner hyperrings, in this hypestructure we deal with to a canonical hypergroup (H, +) with a binary product ., which satisfies the axioms similar a ring. Another importance of canonical is its application to other subjects in mathematics and physics etc. as example above mentioned by Gjergji Zaimi. Another, application is to study the categories of hyperstructures(based on various morphisms, especially multivaled homomorphisms of commutative hypergroups) which these morphisms constitute an structures such as Abelian category (not exactly that) for more study of categories of syperstructures see the following References: [1] R. Ameri, A. Borzooei and M. Hamidi, On categorical connections of hyperrings and rings via the fundamental relation, Int. J. Algebraic Hyperstructures Appl., 1(1) (2014), 108–121. [2] Ameri, R., On categories of hypergroups and hypermodules, Italian Journal of Pure and Applied Mathematics, vol. 6 (2003), 121-132. [3] A CONNECTION BETWEEN CATEGORIES OF (FUZZY) MULTIALGEBRAS AND (FUZZY) ALGEBRAS, italian journal of pure and applied mathematics,208, (2010) 201-208.

I will try to say something about hypergroups  (more generally about the hyperstructures) and hopefully it be useful and can answer to the questions: How is a canonical hypergroup to be thought of as canonical? Are noncanonical hypergroups important? Is there a category theoretic way to see these hyperstructures as natural?

The canonical hypergroups a subclass(or precisely a subcategory of hypergroups) in fact thet are a subclass of polygroup  (or non-commutative hypergroup). One of importance of canonical hypergroup is to constitute Krasner hyperrings, in this hypestructure we deal with to a canonical hypergroup (H, +) with a binary product ., which satisfies the axioms similar a ring. Another importance of canonical is its application to other subjects in mathematics and physics etc. as example above mentioned by Gjergji Zaimi. Another, application is to study the categories of hyperstructures(based on various morphisms, especially multivaled homomorphisms of commutative hypergroups) which these morphisms constitute an structures such as Abelian category (not exactly that).

For more study of categories of hyperstructures see the following References:

[1] R. Ameri, A. Borzooei and M. Hamidi, On categorical connections of hyperrings and rings via the fundamental relation, Int. J. Algebraic Hyperstructures Appl., 1(1) (2014), 108–121.

[2] Ameri, R., On categories of hypergroups and hypermodules, Italian Journal of Pure and Applied Mathematics, vol. 6 (2003), 121-132.

[3] A CONNECTION BETWEEN CATEGORIES OF (FUZZY) MULTIALGEBRAS AND (FUZZY) ALGEBRAS, Italian journal of pure and applied mathematics,208, (2010) 201-208.

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Reza Ameri
Reza Ameri
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I will try to say something about hypergroups( more generally about the hyperstructures) and hopefully it be useful and can answer to the the questions: How is a canonical hypergroup to be thought of as canonical? Are noncanonical hypergroups important? Is there a category theoretic way to see these hyperstructures as natural? The canonical hypergroups a subclass(or precisely a subcategory of hypergroups) in fact thet are a subclass of polygroup( or non-commutative hypergroup). One of importance of canonical hypergroup is to constitute Krasner hyperrings, in this hypestructure we deal with to a canonical hypergroup (H, +) with a binary product ., which satisfies the axioms similar a ring. Another importance of canonical is its application to other subjects in mathematics and physics etc. as example above mentioned by Gjergji Zaimi. Another, application is to study the categories of hyperstructures(based on various morphisms, especially multivaled homomorphisms of commutative hypergroups) which these morphisms constitute an structures such as Abelian category (not exactly that) for more study of categories of syperstructures see the following References: [1] R. Ameri, A. Borzooei and M. Hamidi, On categorical connections of hyperrings and rings via the fundamental relation, Int. J. Algebraic Hyperstructures Appl., 1(1) (2014), 108–121. [2] Ameri, R., On categories of hypergroups and hypermodules, Italian Journal of Pure and Applied Mathematics, vol. 6 (2003), 121-132. [3] A CONNECTION BETWEEN CATEGORIES OF (FUZZY) MULTIALGEBRAS AND (FUZZY) ALGEBRAS, italian journal of pure and applied mathematics,208, (2010) 201-208.