From the book from Calculus to Cohomology, intro remark in Chapter 6 Homotopy. My query is what does the word functorial mean?
2026-03-28 00:06:15.1774656375
What does the sentence 'de rham cohomology is functorial on the category of continuous maps between open sets in Euclidean spaces' mean?
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Assuming this is the book by Madsen and Tornehave, they are referring to the result they prove in Theorem 6.8 (ii). The general concept of "functor" can be found here: https://en.wikipedia.org/wiki/Functor . In Th 6.8 the authors prove de Rham cohomology gives a sequence of functors between the category of open sets of Euclidean space, whose morphisms are homotopy classes of maps, and the category of abelian groups.