Failure of Exactness - Pure Mathematics - Algebra Dictionary Definition A situation where a sequence of homomorphisms ...→A_{i-1}→A_i→A_{i+1}→... fails to be exact at some position i, meaning the image of the incoming map is not equal to the kernel of the outgoing map; homology groups measure this failure.
Failure of Exactness - Pure Mathematics - Algebra Dictionary Definition A situation where a sequence of homomorphisms ...→A_{i-1}→A_i→A_{i+1}→... fails to be exact at some position i, meaning the image of the incoming map is not equal to the kernel of the outgoing map; homology groups measure this failure.