Idea for a new structure: $text{quasi-magma}$ [on hold]
The idea seems outlandish, but I have reasons to be able to introduce it as an idea because I wish a kind of quasi-operation or quasi-function
The operation is just a function. But $+$ is associative and $−$ is not. With $+$ we even have a group
I read from here
In the category-theoretic approach to formal logic, models of theories are usually some sort of functor, and theories themselves are usually made into a category of some sort, possibly together with additional conditions
In actual model definition I cannot 'zooming' to elaborate a better representation to definy a model that describe a good structure for an operation model definition that is jsut a method to use that same operation.
Standard definition
A magma consists of a set equipped with a single binary operation. The binary operation must be closed
I try to extract a quasi-magma definition from Category of magmas or here
the morphisms of magmas are those which preserve the multiplication and the constant.
But..can I imagine this multiplication preservation as a quasi-magma structure or can I say that a quasi-magma is a multiplication that preserve a magmas morphisms?
Another example, this structure is not only a magma but a quasi-group (a magma specialization) is when
the set of integers with respect to subtraction is not a group
because:
The integers equipped with subtraction are both a magma and a
quasigroup. Quasigroups are a specialization of magmas in the same
way that groups are a specialization of magmas. The algebraic
structure $(mathbb{Z},-)$ has inverses, and is thus a quasigroupYou cannot cut or eliminate inverses in your structure; if you
are working with the integers and you are defining subtraction in
the usual way, you will satisfy the axioms of a quasigroup.it's possible for a magma to have only one element that is its
own inverse, yet every other element of the magma has no inverse.The algebraic structure $(mathbb{Z},-)$ has inverses, and is
thus a quasigroup.
But between magma & quasi-group can we imagine a quasi-magma structure ?
magma
asked 2 days ago
Peter Long
134
put on hold as unclear what you're asking by Lord Shark the Unknown, Hans Engler, amWhy, Paul Frost, KReiser yesterday
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
The idea seems outlandish, but I have reasons to be able to introduce it as an idea because I wish a kind of quasi-operation or quasi-function
The operation is just a function. But $+$ is associative and $−$ is not. With $+$ we even have a group
I read from here
In the category-theoretic approach to formal logic, models of theories are usually some sort of functor, and theories themselves are usually made into a category of some sort, possibly together with additional conditions
In actual model definition I cannot 'zooming' to elaborate a better representation to definy a model that describe a good structure for an operation model definition that is jsut a method to use that same operation.
Standard definition
A magma consists of a set equipped with a single binary operation. The binary operation must be closed
I try to extract a quasi-magma definition from Category of magmas or here
the morphisms of magmas are those which preserve the multiplication and the constant.
But..can I imagine this multiplication preservation as a quasi-magma structure or can I say that a quasi-magma is a multiplication that preserve a magmas morphisms?
Another example, this structure is not only a magma but a quasi-group (a magma specialization) is when
the set of integers with respect to subtraction is not a group
because:
The integers equipped with subtraction are both a magma and a
quasigroup. Quasigroups are a specialization of magmas in the same
way that groups are a specialization of magmas. The algebraic
structure $(mathbb{Z},-)$ has inverses, and is thus a quasigroupYou cannot cut or eliminate inverses in your structure; if you
are working with the integers and you are defining subtraction in
the usual way, you will satisfy the axioms of a quasigroup.it's possible for a magma to have only one element that is its
own inverse, yet every other element of the magma has no inverse.The algebraic structure $(mathbb{Z},-)$ has inverses, and is
thus a quasigroup.
But between magma & quasi-group can we imagine a quasi-magma structure ?
magma
asked 2 days ago
Peter Long
134
put on hold as unclear what you're asking by Lord Shark the Unknown, Hans Engler, amWhy, Paul Frost, KReiser yesterday
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
The idea seems outlandish, but I have reasons to be able to introduce it as an idea because I wish a kind of quasi-operation or quasi-function
The operation is just a function. But $+$ is associative and $−$ is not. With $+$ we even have a group
I read from here
In the category-theoretic approach to formal logic, models of theories are usually some sort of functor, and theories themselves are usually made into a category of some sort, possibly together with additional conditions
In actual model definition I cannot 'zooming' to elaborate a better representation to definy a model that describe a good structure for an operation model definition that is jsut a method to use that same operation.
Standard definition
A magma consists of a set equipped with a single binary operation. The binary operation must be closed
I try to extract a quasi-magma definition from Category of magmas or here
the morphisms of magmas are those which preserve the multiplication and the constant.
But..can I imagine this multiplication preservation as a quasi-magma structure or can I say that a quasi-magma is a multiplication that preserve a magmas morphisms?
Another example, this structure is not only a magma but a quasi-group (a magma specialization) is when
the set of integers with respect to subtraction is not a group
because:
The integers equipped with subtraction are both a magma and a
quasigroup. Quasigroups are a specialization of magmas in the same
way that groups are a specialization of magmas. The algebraic
structure $(mathbb{Z},-)$ has inverses, and is thus a quasigroupYou cannot cut or eliminate inverses in your structure; if you
are working with the integers and you are defining subtraction in
the usual way, you will satisfy the axioms of a quasigroup.it's possible for a magma to have only one element that is its
own inverse, yet every other element of the magma has no inverse.The algebraic structure $(mathbb{Z},-)$ has inverses, and is
thus a quasigroup.
But between magma & quasi-group can we imagine a quasi-magma structure ?
magma
asked 2 days ago
Peter Long
134
The idea seems outlandish, but I have reasons to be able to introduce it as an idea because I wish a kind of quasi-operation or quasi-function
The operation is just a function. But $+$ is associative and $−$ is not. With $+$ we even have a group
I read from here
In the category-theoretic approach to formal logic, models of theories are usually some sort of functor, and theories themselves are usually made into a category of some sort, possibly together with additional conditions
In actual model definition I cannot 'zooming' to elaborate a better representation to definy a model that describe a good structure for an operation model definition that is jsut a method to use that same operation.
Standard definition
A magma consists of a set equipped with a single binary operation. The binary operation must be closed
I try to extract a quasi-magma definition from Category of magmas or here
the morphisms of magmas are those which preserve the multiplication and the constant.
But..can I imagine this multiplication preservation as a quasi-magma structure or can I say that a quasi-magma is a multiplication that preserve a magmas morphisms?
Another example, this structure is not only a magma but a quasi-group (a magma specialization) is when
the set of integers with respect to subtraction is not a group
because:
The integers equipped with subtraction are both a magma and a
quasigroup. Quasigroups are a specialization of magmas in the same
way that groups are a specialization of magmas. The algebraic
structure $(mathbb{Z},-)$ has inverses, and is thus a quasigroupYou cannot cut or eliminate inverses in your structure; if you
are working with the integers and you are defining subtraction in
the usual way, you will satisfy the axioms of a quasigroup.it's possible for a magma to have only one element that is its
own inverse, yet every other element of the magma has no inverse.The algebraic structure $(mathbb{Z},-)$ has inverses, and is
thus a quasigroup.
But between magma & quasi-group can we imagine a quasi-magma structure ?
magma
magma
asked 2 days ago
Peter Long
134
asked 2 days ago
Peter Long
134
asked 2 days ago
Peter Long
134
asked 2 days ago
Peter Long
134
asked 2 days ago
Peter Long
134
134
put on hold as unclear what you're asking by Lord Shark the Unknown, Hans Engler, amWhy, Paul Frost, KReiser yesterday
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as unclear what you're asking by Lord Shark the Unknown, Hans Engler, amWhy, Paul Frost, KReiser yesterday
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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