Implication Details
Claim: If a category is cocartesian coclosed and has a strict initial object, then it is thin.
Proof: This follows from the dual implication.
Show 28 categories using this implication
- category of combinatorial species
- category of compact Hausdorff spaces
- category of countable sets
- category of finite sets
- category of finite sets and injections
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of pairs of sets
- category of partially ordered sets
- category of preordered sets
- category of schemes
- category of semigroups
- category of set functions and commutative squares
- category of sets
- category of sets with a distinguished subset
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- category of small categories
- category of smooth manifolds
- category of topological spaces
- category of Z-functors
- walking fork