category of representations

Definition 0.1.

The category $Rep({\\mathsf{G}})$ of representations has objects the representations of a groupoid ${\\mathsf{G}}$ , and as morphisms the intertwiners $i:\\rho_{j}\\longrightarrow\\rho_{k}$ that are (vector) bundle morphisms $i:E\\longrightarrow E$ over the manifold $M$ so that $\\rho_{k}(g)\\circ i=i\\circ\\rho_{j}$ . Because representations are functors $\\rho:{\\mathsf{G}}\\longrightarrow{\\bf Vect}$ , an itertwiner $i$ is in fact a natural transformation between two such functors that are groupoid representations of ${\\mathsf{G}}$ , in this case implemented via the vector bundle morphisms $i:E\\longrightarrow E$ .

单词	CategoryOfRepresentations
释义	category of representations Definition 0.1. The category $Rep({\\mathsf{G}})$ of representations has objects the representations of a groupoid ${\\mathsf{G}}$ , and as morphisms the intertwiners $i:\\rho_{j}\\longrightarrow\\rho_{k}$ that are (vector) bundle morphisms $i:E\\longrightarrow E$ over the manifold $M$ so that $\\rho_{k}(g)\\circ i=i\\circ\\rho_{j}$ . Because representations are functors $\\rho:{\\mathsf{G}}\\longrightarrow{\\bf Vect}$ , an itertwiner $i$ is in fact a natural transformation between two such functors that are groupoid representations of ${\\mathsf{G}}$ , in this case implemented via the vector bundle morphisms $i:E\\longrightarrow E$ .
随便看	BoubakerPolynomials Boubaker Polynomials BoundaryFrontier boundary / frontier BoundaryOfAClosedSetIsNowhereDense boundary of a closed set is nowhere dense BoundaryOfAnOpenSetIsNowhereDense boundary of an open set is nowhere dense Bounded bounded bounded Bounded1 BoundedComplete bounded complete BoundedFunction bounded function BoundedInverseTheorem bounded inverse theorem BoundedLattice bounded lattice BoundedLinearExtensionOfAnOperator bounded linear extension of an operator BoundedLinearFunctionalsOnLinftymu BoundedLinearFunctionalsOnLpmu bounded linear functionals on L^p⁢(μ)