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additiondiscussionlibrary-designstatus: duplicateThe main contents of the issue or PR already exists in another issue or PR.The main contents of the issue or PR already exists in another issue or PR.
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Discussing @Taneb 's most recent comments on PR #1767 , it is clear that we are (also!) missing some fairly crucial definitions from the Algebra
library/hierarchy: ie given a XHomomorphism h
, define
- kernel, ie via the property
InKernel = λ x → h x ≈ 0
(suitably interpreted) - image, ie via the property
InImage = λ y → ∃ x → h x ≈ y
together with their evident closure properties as substructures, cf. issue #1899 .
Note also that while we have definitions of structures (but not yet bundles! #1960) defining IsXMonomorphism
and IsXIsomorphism
based on Function.Definitions.Injective
and Function.Definitions.Core2.Surjective
, these might better (best?) be rephrased/proved equivalent to, properties involving the kernel and image, eg.
IsXMonomorphism h
iff∀ {x} → InKernel h x → x ≈ 0
, etc.
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additiondiscussionlibrary-designstatus: duplicateThe main contents of the issue or PR already exists in another issue or PR.The main contents of the issue or PR already exists in another issue or PR.