and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
A differential object in a category with translation $T : C \to C$ is an object $V$ equipped with a morphism $d_V : V \to T V$.
Usually, when addressing coalgebras for $T$ as differential objects one considers these in additive categories and requires that they are nilpotent in that $V \stackrel{d_V }{\to} T V \stackrel{T d_V}{\to} T T V$ is the zero morphism. Such a differential object is called a chain complex.
In a differential object $d_V : V \to T V$ in an additive category $C$ the shifted differential object is $T V$ with differential given by $d_{T V} = - T(d_V)$. The minus sign here is crucial in many constructions such as that of the mapping cone. It is naturally understood in terms of fiber sequences in stable infinity-categories.
Last revised on March 17, 2011 at 10:41:40. See the history of this page for a list of all contributions to it.