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For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.

9 votes
Accepted

Homology of simplicial complex versus homology of simplicial _set_

There is a problem with your definition of the boundary map $\partial : C_q(K)\to C_{q-1}(K)$. The formula $\partial _i[v_0,\cdots,v_q]=[v_0,\cdots,v_{i-1},v_{i+1},\cdots,v_q]$ depends on an orderin …
Allen Hatcher's user avatar
11 votes
Accepted

Simplicial complexes vs. geometric realization of abstract simplicial complexes

At least in the realm of topology an abstract simplicial complex is equivalent to a topological (or geometric) simplicial complex, and neither of these two notions involves anything about orienting th …
Allen Hatcher's user avatar