On the 4-clifford algebra in abstract differential geometry

In this research paper, differential triads over a topological space X are defined as objects of the Cartesian product category Alg×_X F^d ×_X DMod over the same fixed topological space X. From differential triads sheaves (A_iX 〖 ,∂_iX,Ω〗_iX ) and (A_jX 〖 ,∂_jX,Ω〗_jX ) we defined morphisms of differential triads using a differential morphism ∂^ij:H_A^ij→H_Ω^ij, where H_A^ij=〖Hom〗_(〖Alg〗_X ) (A_iX,A_jX ) and 〖 H〗_Ω^ij=〖Hom〗_(〖DMod〗_X ) (Ω_i,Ω_j ). From the quadratic forms, we determined quadratic differential triads and Clifford differential triads.