Weights for Objects of Monoids

Łukasz Sienkiewicz
Tuesday, July 23, 2013 - from 16:00 to 16:25
Weighted limits and colimits provide a uniform way to define many interesting operations on $2$-categories. It is known for more than 40 years that the Eilenberg-Moore object for a monad in any 2-category can be expressed as a weighted limit. In this talk I will show that the object of monoids over any monoidal category object in any 2-category can be also defined as a weighted limit. I will describe in a systematic way how matrices of symmetric (possibly colored) operads can be used to define this weight and many similar ones: like the weight for the object of bi-monoids over a symmetric monoidal category or the weight for the object of actions of monoids along an action of a monoidal category. (Joint work with Marek Zawadowski.)