Holmstrom Adjoint functor

“A left adjoint is right exact”

In general, a left adjoint preserves colimits, and a right adjoint preserves limits.

http://mathoverflow.net/questions/6376/why-forgetful-functors-usually-have-left-adjoint

Examples of adjoints: (left adjoint, right adjoint)

• (geom. realization, sing)
• Lots of examples in Weibel (via index)
• “Informally, a free functor is a left adjoint to a forgetful functor”

nLab page on Adjoint functor