Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
Let be an (∞,1)-category and an object.
A subobject of is a 1-monomorphism into .
The (∞,1)-category of subobjects of is the -truncation of the slice-(∞,1)-category of over
This is the category whose objects are monomorphisms in and whose morphisms are 2-morphisms
in .
is a (0,1)-category (a poset).
This appears for instance in (Lurie, section 6.2).
If is a locally presentable (∞,1)-category then is a small category.
subobject in an -category
Last revised on December 4, 2012 at 00:57:53. See the history of this page for a list of all contributions to it.