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	all solution of the Lorenz equation enter an ellipsoid AllUnnaturalSquareRootsAreIrrational All unnatural square roots are irrational AlmostCocommutativeBialgebra almost cocommutative bialgebra AlmostComplexStructure almost complex structure AlmostContinuousFunction almost continuous function AlmostConvergent almost convergent AlmostConvex almost convex AlmostEverywhere almost everywhere AlmostPerfectNumber almost perfect number AlmostPeriodicFunctionclassicalDefinition almost periodic function (classical definition) AlmostPeriodicFunctionequivalentDefinition almost periodic function (equivalent definition) AlmostSurelyAbsolutelyBoundedRandomVariable almost surely absolutely bounded random variable AlonChungLemma Alon-Chung lemma