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Results tagged with infinity-categories
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user 148161
Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
1
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0
answers
254
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Homotopy coherent nerve for algebraic model categories
Is a homotopy coherent nerve defined for algebraic model category that returns algebraic quasi-categories as Urs Schreiber wrote about? Or do we not know how to determine it / does it seem impossible? …
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6
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0
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121
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Treatment of classes of mono/epi morphisms in $(\infty, 1)$-categories
In the classical theory of $(1, 1)$ categories, the chain of classes of mono/epi morphisms is well known: plain $\leftarrow$ strong $\leftarrow$ effective $\leftarrow$split ((I assume that the categor …
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4
votes
1
answer
359
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Is the concept of an $H$ object still interesting, when we have the $\infty$-version of it?
Recently I got acquainted with $\infty$-algebraic theories. I expect $\infty$-algebraic objects (of ordinary Lawvere theories) in $\infty\text{-}\mathrm{Groupoid}$ to behave much better than algebraic …
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2
votes
1
answer
446
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Why do we need enriched model categories?
As far as I understand, model categories mainly provide tools for studying the "homotopy theories" (that is, $\infty$-categories) that are ubiquitous in mathematics. From this point of view, model cat …
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3
votes
1
answer
427
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Does the concept of a $\infty$-category have a natural definition in the $\infty$-world?
I start with a thesis: the natural notion of equality is additional data (paths/morphisms), not a binary relation (the fact that they exist). So, in particular, with such a constructivization (replaci …
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5
votes
1
answer
278
views
Do finitely presentable $\infty$-groupoids precisely correspond to the finite cell complexes?
In the Higher Topos Theory, Example 1.2.14.2 says “finitely presentable $\infty$-groupoids correspond precisely to the finite cell complexes” But, for example, $K(\mathbb{Z}, 2)$ is seems finitely pre …
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7
votes
1
answer
256
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Finitely presentable objects in the categories of algebras of $\infty$-algebraic theories
By default, all terms are understood in the infinity sense (“category” means “$(\infty, 1)$-category”, etc.).
An object $A$ in a category is said to be finitely presentable (or compact) if the functor …
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6
votes
1
answer
256
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Reference: the category of derived affine schemes is extensive
The category (that is, $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences.
See extensive category. Does …
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5
votes
0
answers
209
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What do we know about effective epimorphisms of derived affine schemes/manifolds?
By default, all terms are understood in the infinity sense (“category” means “(∞,1)-category”, etc.)
Recall that the morphism $X \to Y$ is an effective epimorphism if the Čech diagram
$$ ... \to X \ti …
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9
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What is the exact definition of the $\infty$-topos of sheaves on a localic $\infty$-groupoid?
The category $\mathrm{Locale}$ is equivalent to the category $0\text{-}\mathrm{Topos}$ .
The 2-category $\mathrm{LocalicGroupoid}$ (with suitable localization) is equivalent to the 2-category $1\text …
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