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A sequence of morphisms in which the image of each map equals the kernel of the next.
wp-exact-sequencenlab-exact-sequencehatcher-algebraic-topologystacks-derived-textEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
An exact category comes with a specified class of kernel–cokernel pairs, called conflations; retaining one such pair gives an exact sequence in the chosen exact structure.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
stacks-derived-textEach relation below starts 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-topology