as objects, the 1-morphisms in ;
as 1-morphisms from to , the pairs where is a 1-morphism in and is a 2-isomorphism in .
as 2-morphisms from to , the 2-morphisms such that .
If is a strict 2-category, then so is . Moreover, in this case, we can also define the strict-slice 2-category to be the subcategory of containing all the objects, only those morphisms such that is an identity, and all 2-morphisms between these.
If, on the other hand, we do not require to be invertible, then we obtain the lax-slice 2-category (with evident dual the colax-slice 2-category).
Finally, the subcategory of whose objects are the fibrations and whose morphisms are the maps of fibrations is denoted , and may be called the fibrational-slice 2-category. Similarly we have the opfibrational-slice .
When is a 1-category, the slice, strict-slice, lax- and colax-slice, and fibrational- and opfibrational-slice 2-categories all coincide with the usual slice category. When is a (2,1)-category, then all of them coincide except the strict one. Thus, when generalizing a concept involving slice categories from categories to 2-categories, it can sometimes be a little subtle to decide on the correct version of slice category to use.