Are bicategories and lax 2-categories the same?

Question

My question is that whether the definition of bicategories is the same as the definition of lax 2-categories.

I heard that they are both week versions of 2-categories.

Are they the same? If not, how do they differ?

I would like to know answers and reference that defines these definitions rigorously.

Thank you.

Answer 1

Leinster introduced a lax bicategory (def. 3.4.1) -- in an unbiased manner --, which is even more lax than a normal bicategory, in that the coherence morphisms in there are not assumed to be isomorphisms.