Post date: 25-sep-2015 1:36:54
In this talk we will continue in the enriched setting and motivate the definition of weighted limit. In particular, we will focus on the case V=Cat, and study special phenomena that occur under this assumption.
We will follow Kelly's treatment of limits of category-valued functors in 'Elementary Observations on 2-Categorical Limits'. In this situation, we will be able to prove that Cat is a bicomplete Cat-category, and show explicit constructions for a general weighted 2-limit in an arbitrary (strict) 2-category that require the existence of a more restricted class of limits. We will also introduce the less rigid notions of pseudolimit, lax limit, and bilimit and prove that in certain cases these reduce to ordinary weighted limits.