We study cocompleteness, co-wellpoweredness, and generators in the centralizer category of an object or morphism a monoidal category, center weak category. explicitly give some answers for when colimits, these categories can be inherited from their base monidal categories. Most importantly, we investigate cofree objects comonoids

We take another look at the Chu construction and show how to simplify it by looking at it as a module category in a trivial Chu category This simpli es the construction substantially especially in the case of a non symmetric biclosed monoidal category We also show that if the original category is accessible then for any of a large class of polynomial like functors the category of coalgebras has...

This note will be for the most part of an expository nature; many of the results here have appeared elsewhere. We would like however, to highlight the connection between Jim Stasheff’s early work on A∞ algebras in the 1960’s and the notion of sh Lie algebras (L∞ algebras) which is currently popular in mathematical physics; see, for example, [1] and [7]. This connection involves some work of Vic...