nLab
locally small (infinity,1)-category (changes)
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**
(∞,1)-category theory**
**Background**
*
category theory
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higher category theory
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(n,r)-category
**Basic concepts**
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(∞,1)-category
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hom-objects
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equivalences in/
of $(\infty,1)$-categories
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sub-(∞,1)-category
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reflective sub-(∞,1)-category
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reflective localization
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opposite (∞,1)-category
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over (∞,1)-category
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join of quasi-categories
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(∞,1)-functor
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exact (∞,1)-functor
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(∞,1)-category of (∞,1)-functors
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(∞,1)-category of (∞,1)-presheaves
* **
fibrations**
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inner fibration
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left/right fibration
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Cartesian fibration
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Cartesian morphism
**Universal constructions**
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limit
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terminal object
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adjoint functors
**Local presentation**
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locally presentable
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essentially small
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locally small
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accessible
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idempotent-complete
**Theorems**
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(∞,1)-Yoneda lemma
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(∞,1)-Grothendieck construction
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adjoint (∞,1)-functor theorem
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(∞,1)-monadicity theorem
**Extra stuff, structure, properties**
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stable (∞,1)-category
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(∞,1)-topos
**Models**
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category with weak equivalences
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model category
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derivator
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quasi-category
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model structure for quasi-categories
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model structure for Cartesian fibrations
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relation to simplicial categories
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homotopy coherent nerve
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simplicial model category
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presentable quasi-category
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Kan complex
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model structure for Kan complexes
Contents
Idea
The notion of locally small -category is the generalization of the notion of locally small category from category theory to (∞,1)-category theory.
Definitions
This appears as HTT, below prop. 5.4.1.7.
Properties
Created on April 14, 2010 at 18:20:09.
See the history of this page for a list of all contributions to it.