nLab
(infinity,2)-site

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Context

$(∞, 2)$ -Category theory

2-category theory

Definitions

2-category
strict 2-category
bicategory
enriched bicategory

Transfors between 2-categories

2-functor
2-natural transformation?
- lax natural transformation
- icon
modification
Yoneda lemma for bicategories

Morphisms in 2-categories

fully faithful morphism
faithful morphism
conservative morphism
pseudomonic morphism
discrete morphism
eso morphism

Structures in 2-categories

adjunction
mate
monad
cartesian object
fibration in a 2-category
codiscrete cofibration

Limits in 2-categories

2-limit
2-pullback
comma object
inserter
inverter
equifier

Structures on 2-categories

2-monad
monoidal 2-category
- cartesian bicategory
Gray tensor product
proarrow equipment

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$(∞, 2)$ -Topos theory

(∞,2)-topos

(∞,2)-presheaf, (∞,2)-site,

(∞,2)-sheaf

codomain fibration, tangent (∞,1)-category, quasicoherent ∞-stack

Truncations

2-pretopos
2-presheaf, 2-site, 2-sheaf, stack
n-localic 2-topos
2-Giraud theorem

(2,1)-topos

(2,1)-presheaf, (2,1)-site, (2,1)-sheaf

(∞,1)-topos

(∞,1)-presheaf, (∞,1)-site, (∞,1)-sheaf

presheaf, site, sheaf

An (n,r)-site for $n = ∞$ , $r = 2$ .

Created on March 9, 2012 18:51:04 by Urs Schreiber (82.113.106.131)

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