Jan 17, 2021
Direct sum is not the coproduct in the category of quadratic vector spaces. The absence of terminal objects and (co)products in QVec is due to the fact that projections do not generally preserve norms.
José Figueroa O'Farrill, Spin Geometry
#category theory#vectors#vector space#tangent bundle#manifolds#frames#bilinear#quadratic form#quadratic forms#symmetric#functional#polar#polarisation#change of variables#trivial object#categories#terminal objects#coproducts#morphisms#maps#norms#Clifford algebra#William Kingsdon Clifford#degenerate#grading#graded algebra#projection#projections#t-norms#maths