Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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Cones form a functor in every triangulated category
Statement
The triangulated axioms canonically supply a functor assigning a cone to each morphism.
Refutation
Given: The displayed data.
TR1 supplies a completion for each morphism, but its third object is only determined up to nonunique isomorphism.
TR3 likewise supplies, rather than canonically chooses, maps between completions; therefore the axioms do not provide compatible object and morphism choices. An enhancement is extra structure.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Amnon Yekutieli, A Course on Derived Categories, Remark after Definition 8.1.2 (standard reference, not scraped)