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Definitions from the Web

Morphism

Definition:

A morphism refers to a structure-preserving map or function between two mathematical objects. It is commonly used in various branches of mathematics such as algebra, topology, and category theory.

Examples:

Noun:

In group theory, a group homomorphism is a morphism that preserves the algebraic structure between two groups.

Example sentence: The morphism between the symmetric group and the alternating group is a well-known isomorphism.

Noun:

In category theory, a morphism is an arrow or an object in a category, representing a relationship between two objects.

Example sentence: The composition of two morphisms in a category can result in another morphism.

Adjective:

In graph theory, a morphism is used to describe a mapping between two graphs that preserves edges and vertices.

Example sentence: The graph morphism ensures that the connectedness of the original graph is preserved in the transformed graph.

Possible related products on Amazon:

• Group theory books
• Category theory textbooks
• Graph theory resources