This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are derived from the unbounded case.
Keywords: operads, cofree coalgebras
2000 MSC: 18G55, 55U40
Theory and Applications of Categories, Vol. 25, 2011, No. 8, pp 189-246.