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In the additivity axiom, is the symbol supposed to represent disjoint union, or one-point union, or what? The notation should be named in plain English. If it's disjoint union, then isn't a more popular (and less overloaded) choice?
Joshua Davis22:39, 3 April 2006 (UTC)reply
Can someone explain how exactly is a natural transformation? I think its supposed to be called the informal "natural map" instead of transformation because is evaluated at (X,A) whereas is evaluated at (A,Ø), a transformation is suppose to have both functor evaluate at the same point.
Money is tight (
talk)
05:45, 12 January 2011 (UTC)reply
Yes, I was asking myself the same question and found an answer in Eilenberg's book (Samuel Eilenberg, Norman E. Steenrod, Foundations of algebraic topology,
Princeton University Press, Princeton, New Jersey, 1952.) in chapter IV.7 (page 113). There a functor T from the category of topological pairs to the category Top, such that and , is defined. Then the (correct) statement is, that the boundary operator is a natural transformation from to the composite functor . --
Quiet photon (
talk)
11:25, 28 April 2011 (UTC)reply
Milnor's paper should be cited, and a reference to the derived functor of inverse limits should also be included.
This is kind of a big deal these days. (:+{)} Drwonmug 17:55, 6 October 2023 (UTC) — Preceding
unsigned comment added by
Drwonmug (
talk •
contribs)
Minor excision detail
The subset U in the excision axiom doesn't need to be open, right? It is just the setting in which E-S formulated the axioms, and I haven't seen this requirement in most modern mentions of E-S axioms and don't see why it would be needed...
2601:184:407F:E100:1424:FA66:51E0:F379 (
talk)
04:21, 1 June 2020 (UTC)reply