left exact
A functor is left exact when it preserves finite limits.
- Dual property: right exact
- nLab Link
Relevant implications
- cofinitary andleft exact implies continuous *
- equalizer-preserving andfinite-product-preserving implies left exact *
- exact is equivalent to left exact andright exact
- left exact implies finite-product-preserving andterminal-object-preserving
- left exact implies monomorphism-preserving
*Those implications also require assumptions on the source or target category.
Examples
There are 3 functors with this property.
- contravariant power set functor
- forgetful functor for vector spaces
- identity functor on the category of sets
Counterexamples
There are 3 functors without this property.
Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
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