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Stream: theory: category theory

Topic: lax limits are weighted 2-limits

Matteo Capucci (he/him) (Nov 12 2020 at 11:36):

On the nlab page about 2-limits it is claimed that

This may look like a different concept, but in fact, for any weight $J$ there is another weight $Q_l(J)$ such that lax $J$-weighted limits are the same as $Q_l(J)$-weighted 2-limits. Here $Q l$ is the lax morphism classifier for 2-functors. Therefore, lax limits are really a special case of 2-limits. Similarly, oplax limits, in which we use oplax natural transformations, are also a special case of 2-limits.

Does anyone know how is $Q_l$ defined or a reference to substantiate this claim?

Nathanael Arkor (Nov 12 2020 at 14:29):

I believe the standard reference is Kelly's Elementary Observations on 2-Categorical Limits (see Prop. 5.2).

Matteo Capucci (he/him) (Nov 12 2020 at 18:18):

Thanks!!