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A contravariant functor from the simplex category to sets.
Precisely a simplicial object in Set.
wp-simplicial-setnlab-simplicial-sethatcher-algebraic-topologyEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A simplicial object in Set is precisely a simplicial set; this changes the ambient target category rather than imposing an internal axiom.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-simplicial-setnlab-simplicial-sethatcher-algebraic-topologyEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Geometric realization canonically constructs a topological space from a simplicial set ; together with the singular complex it relates the corresponding homotopy theories.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
hatcher-algebraic-topology