Category theory MOC

Slice category

Let be a category and . The slice category is defined as follows:¹ cat

• for and .
• is a morphism such that the following diagram commutes:

Typically the objects are referred to by the morphism (e.g. ) only. A slice category is a special case of a Comma category.

Properties

• There exists a functor that forgets the base object.

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Footnotes

1. 2010. Category theory, p. 16 ↩