Simplicial Homology and Cohomology in the Context of Chain Complexes

4 Simplicial Homology and Cohomology in the Context of Chain Complexes 

Let us now return to the simplicial context. For any trisp A, the algebraic structure introduced in Subsection 3.2.3, and more generally in Subsection 3.4.2, can be summarized as a sequence of 72 -modules and 72 -module homomorphisms 

This one is called a simplicial cochain complex of A with coefficients in IZ, and is denoted hy C A, TZ. The cohomology groups of this cochain complex as defined in Subsection 3.4.3 coincide with the simplicial cohomology groups 

Finally, we mention that we also have the augmented simplicial chain complex of A with coefficients in TZ  

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