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In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
A class (), whose elements are called morphisms or maps or arrows. Each morphism f {\displaystyle f} has a source object a {\displaystyle a} and target object b {\displaystyle b} . The expression f : a ↦ b {\displaystyle f:a\mapsto b} would be verbally stated as " f {\displaystyle f} is a morphism from a to b ".
A category C consists of two classes, one of objects and the other of morphisms.There are two objects that are associated to every morphism, the source and the target.A morphism f from X to Y is a morphism with source X and target Y; it is commonly written as f : X → Y or X Y the latter form being better suited for commutative diagrams.
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
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Nannie Doss confessed to killing four of her husbands, her mother, sister, two of her children, two of her grandsons, and a mother-in-law over a 27-year killing spree
Using textbook sharing, students share the physical textbook with other students, and the cost of the book is divided among the users of the textbook. Over the life of the textbook, if 4 students use the textbook, the cost of the textbook for each student will be 25% of the total cost of the book.