A differential graded algebra (or simply DGA) A is a graded algebra equipped with a map which is either degree 1 (cochain complex convention) or degree (chain complex convention) that satisfies two conditions:
- (i)
- This says that d gives A the structure of a chain complex or cochain complex (accordingly as the differential reduces or raises degree).
- (ii) .
- This says that the differential d respects the graded Leibniz rule.
Read more about Differential Graded Algebra: Examples of DGAs, Other Facts About DGAs
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