Journal article
Some exact sequences for the homotopy (bi-)module of a monoid

Publication Details
Kobayashi, Y.; Otto, F.
Publication year:
International Journal of Algebra and Computation
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Volume number:

For finitely presented monoids the homological finiteness conditions left-FP3, left-FP4, right-FP3 and right-FP4, the homotopical finiteness conditions of having finite derivation type FDT and of being of finite homological type FHT are developed and the relationship between these notions is investigated in detail. In particular, a result of Pride [40] and Guba and Sapir [27] on the exactness of a sequence of bimodules for the homotopy module is proved in a completely different, purely combinatorial manner. This proof is then translated into a proof of the corresponding result for the left homotopy module, thus giving new insights into the relationship between the finiteness conditions considered.


Last updated on 2019-24-07 at 08:54