Search Results

Then the equivariant derived category of sheaves $D^b_{eq}([G\backslash X]_{\cdot})$ is defined to be the full subcategory of $D^b([G\backslash X]_{\cdot})$ consisting of complexes of simplicial sheaves … $$ If we defined the equivariant derived category as the full subcategory with Cartesian cohomologies, then is it equivalent to the previous definition? …

Is there any references for the structure of the equivariant K-theory $K_{S^1}(S^2)$ where the action of $S^1$ on $S^2$ is defined to be rotation about the $z$-axis? …

We denote the category of $G$-equivariant sheaves on $X$ by $\text{Sh}_G(X)$. … An equivariant sheaf $(\mathcal{I},\eta)$ is called injective if for any monomorphsim of equivariant sheaves $\phi: (\mathcal{F},\theta)\to (\mathcal{G},\xi)$ and any morphism of equivariant sheaves $\ …

Then the category of equivariant complex vector bundles on $X$, $\text{Vect}_G(X)$, is equivalent to the category $\text{Vect}(X/G)$ consists of complex vector bundles on the quotient space $X/G$. … The category of equivariant $A$-modules consists of $M$ such that $M\cong M^g$ as $A$-modules for any $g\in G$ and the morphisms are $G$- equivariant $A$-module maps. …