The category of differential graded commutative algebras over a field of characteristic 2 seems to have some not so nice properties. I could not find an answer in StackExchange as to why this category is not abelian(and would appreciate a reference),but the purpose of this question is to try to find a workaround, if possible. Start with a graded commutative differential polynomial algebra $A$, with differential $d$, and a homogeneous element $w$,which is a cycle i.e. $d(w) = 0$. Call $I$ the ideal generated by $w$, and there should be a short exact sequence $0 \to K \to A \to A/I \to 0 $, leading to a long exact sequence in homology, allowing me to determine at least most of the homology of the quotient from the cohomology of $A$. A specific example, where maybe less things go wrong is the following: $A = Z/2Z[a,b,c,x,y,z]$, where the a, b, and c have degree 1, and x, y,and z have degree 2, and the differential d makes x, y, and z cycles, i.e. d(x) = d(y) = d(z) = 0.
Any help or references would be appreciated.
