A bicategory has objects, hom-categories, composition functors and identity 1-cells. Associativity and unit laws hold through coherent invertible 2-cells, satisfying pentagon and triangle identities. A monoidal category is exactly a bicategory with a single object: its objects are the 1-cells, its morphisms the 2-cells, and its tensor product the horizontal composition.
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A bicategory is a generalization of the concept of a category in category theory. While a category consists of objects and morphisms (arrows) between those objects, a bicategory includes not only objects and morphisms but also "2-morphisms" (which can be thought of as arrows between arrows). Here are the key features of a bicategory: 1. **Objects**: Just like in categories, a bicategory has objects.