well-copowered
A category is well-copowered if the collection of quotients of any object is isomorphic to a set.
- Dual property: well-powered
- nLab Link
Relevant implications
essentially small implies well-powered and well-copowered and locally essentially small
triviallocally presentable implies locally essentially small and well-powered and well-copowered and complete and cocomplete and generator
For the non-trivial conclusions see Adamek-Rosicky, Thm. 1.20, Cor. 1.28, Rem. 1.56, Thm. 1.58.elementary topos and locally essentially small implies well-copowered
This follows from Mac Lane & Moerdijk, Theorem IV.7.8 (and Prop. I.3.1).groupoid implies self-dual and epi-regular and pushouts and filtered colimits and right cancellative and well-copowered
[dualized] easyself-dual and well-powered implies well-copowered
trivial by self-dualityself-dual and well-copowered implies well-powered
trivial by self-duality
Examples
- category of abelian groups
- category of Banach spaces with linear contractions
- category of combinatorial species
- category of commutative rings
- category of finite abelian groups
- category of finite orders
- category of finite sets
- category of finite sets and bijections
- category of finite sets and injections
- category of finite sets and surjections
- category of finitely generated abelian groups
- category of free abelian groups
- category of groups
- category of left R-modules
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with ∞ allowed
- category of metric spaces with non-expansive maps
- category of monoids
- category of non-empty sets
- category of pointed sets
- category of posets
- category of rings
- category of rngs
- category of sets
- category of sets and relations
- category of simplicial sets
- category of small categories
- category of smooth manifolds
- category of topological spaces
- category of vector spaces
- delooping of a non-trivial finite group
- delooping of an infinite group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- empty category
- partial order [0,1]
- partial order of extended natural numbers
- partial order of natural numbers
- preorder of integers w.r.t. divisiblity
- trivial category
- walking isomorphism
- walking morphism
- walking parallel pair of morphisms
Counterexamples
Unknown
For these categories the database has no info if they satisfy this property or not.