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Results tagged with topos-theory
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user 429204
A topos is a category that behaves very much like the category of sets and possesses a good notion of localization. Related to topos are: sheaves, presheaves, descent, stacks, localization,...
14
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2
answers
681
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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 …
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11
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1
answer
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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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2
answers
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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 …
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6
votes
Topos-theoretic Galois theory
Maybe you would like to see the thesis of O. Leroy, Groupoïde fondamental et théorème de Van Kampen en théorie des topos, available from https://plmbox.math.cnrs.fr/f/7ffa366379144dd4bacc/?dl=1 — the …
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5
votes
1
answer
278
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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 …
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3
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Making the étale topos construction a fully faithful 2-functor from schemes to Grothendieck ...
Take a look at the paper of Barwick, Glasman and Haine (https://arxiv.org/pdf/1807.03281.pdf).
In particular the section "Exodromy for schemes & the Reconstruction Theorem".
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0
answers
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The site and the space
There is a (seemingly simple) statement in the literature on sheaf theory, namely,
If $E$ is the site of opens of a topological space $X$, the notion of sheaf over $X$ coincides with that of sheaf of …
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3
votes
4
answers
534
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Phenomena of topos
These days I am wandering on a wild adventure in an incredible but intimidating land. Fortunately, I could find a guide to some animals of this land
Phenomena of gerbes
But someone said to me that thi …
1
vote
1
answer
146
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"Variable and fixed" in categories
We often find in Grothendieck terminology the words variable and fixed (or absolute).
For example in SGA 4 studies variable topological spaces, groups, and categories as examples of morphisms of topos …
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0
answers
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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 …
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Defining properties of categories out of an indicial category
$\newcommand{\Hom}{\operatorname{Hom}}$Suppose we want to define the category of arrows of $S$. Below are two forms of doing it.
Definition 1: If $D$ is of the following type: $\bullet \to \bullet$, …
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Grothendieck's manuscript on topology
There is an article where you can find some ideas about this.
Towards a new geometry of forms
In: The notion of space in Grothendieck: from schemes to a geometry of forms,
John Alexander Cruz Morale …