In
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
, especially
category theoryIn mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects linked in diagrams by morphisms or arrows....
, a
discrete category is a category whose only
morphismIn mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures.The study of morphisms and of the structures over which they are defined, is central to category theory...
s are the identity morphisms. It is the simplest kind of category. Specifically a category
C is discrete if
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In
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
, especially
category theoryIn mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects linked in diagrams by morphisms or arrows....
, a
discrete category is a category whose only
morphismIn mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures.The study of morphisms and of the structures over which they are defined, is central to category theory...
s are the identity morphisms. It is the simplest kind of category. Specifically a category
C is discrete if