Implication Details
Claim: If a category is total, then it is complete.
Proof: This is proven in G. M. Kelly, A survey of totality for enriched and ordinary categories, Thm. 5.6.
Show 14 categories using this implication
- category of finitely generated abelian groups
- simplex category
- category of fields
- category of groups
- category of countable groups
- partially ordered collection of ordinal numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of non-empty sets
- category of vector spaces
- category of large vector spaces over a large field with a small basis
- cocompletion of a discrete–pair join
- forked commutative square
- walking coreflexive pair
- walking parallel pair