In mathematics, especially category theory, a double category is a generalization of a category where instead of morphisms, we have vertical morphisms, horizontal morphisms and 2-morphisms. Introduced by Ehresmann in 1960s, the notion may be compared with that of a bicategory; namely, the notion of a bicategory is obtained by enrichment, while the notion of a double category is obtained by internalization.
In mathematics, especially category theory, a double category is a generalization of a category where instead of morphisms, we have vertical morphisms, horizontal morphisms and 2-morphisms. Introduced by Ehresmann in 1960s, the notion may be compared with that of a bicategory; namely, the notion of a bicategory is obtained by enrichment, while the notion of a double category is obtained by internalization.
Source: Wikipedia "Double category" · CC BY-SA 4.0
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