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Results tagged with homotopy-theory
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user 429204
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
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Kan extensions in Grothendieck school
Considering both the ubiquity of Kan extensions in category theory (as MacLane stated, 'The notion of Kan extensions subsumes all the other fundamental concepts of category theory.'), its early introd …
- 894
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2
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Who introduced the notion of 2-categories?
Wikipedia seems to have an answer
"The concept of 2-category was first introduced by Charles Ehresmann in his work on enriched categories in 1965. The more general concept of bicategory (or weak 2-cat …
- 10.6k
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Derivators (in English)
Maybe you should try Grothendieck himself
T. Hosgood has translated a letter from Grothendieck to R. Thomason where he gave the motivation for the theory
https://labs.thosgood.com/translations/grothen …
- 894
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Axioms of derivators
I would like to enter the world of derivators. We can find a little history here and there about the limitations of triangulated categories and the motivation to enhance them, but also to compute homo …
- 3,411
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Indexing categories of derivators
It is not clear to me the role of the domain and target in the definition of prederivators.
For instance, the classical references put the domain as $\mathit{Dia}$, others as $\mathit{Cat}$ itself.
So …
- 3,411
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A non-conventional definition of topoi
In "Toward a Galoisian interpretation of homotopy theory" (2000), B. Toën wrote:
Pour expliquer notre point de vue sur la notion de champs rappelons une construction (non conventionnelle) du topos de …
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