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An exact sequence extending through many degrees, commonly produced by a short exact sequence of complexes, a pair of spaces, or a fibration.
wp-exact-sequencehatcher-algebraic-topologyEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A long exact sequence is an exact sequence indexed across successive degrees, usually linked by connecting homomorphisms.
The target is a member or subtype of the broader source class.
hatcher-algebraic-topologyThis is an authored directed relation from the source endpoint to the target endpoint.
The canonical short exact sequence involving a mapping cone induces a long exact sequence in homology, relating the source, target, and cone of the map.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
hatcher-algebraic-topologystacks-derived-categoryThis is an authored directed relation from the source endpoint to the target endpoint.
A pair produces long exact sequences relating , , and .
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-topologyEach relation below starts at this concept.
No direct relations are authored in this direction.