Formal criteria for adjoint functors explained
In category theory, a branch of mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor.
One criterion is the following, which first appeared in Peter J. Freyd's 1964 book Abelian Categories, an Introduction to the Theory of Functors:Another criterion is:
See also
Bibliography
- Book: Mac Lane, Saunders . Categories for the Working Mathematician. 17 April 2013. Springer Science & Business Media. 978-1-4757-4721-8.
- Book: Borceux . Francis. 10.1017/CBO9780511525858.005 . Adjoint functors . Handbook of Categorical Algebra . 1994 . 96–131 . 978-0-521-44178-0 .
- Freyd . Peter . Abelian categories . Reprints in Theory and Applications of Categories . 2003 . 3 . 23–164 .
- 10.1215/ijm/1256052605 . The adjoint functor theorem and the Yoneda embedding . 1971 . Ulmer . Friedrich . Illinois Journal of Mathematics . 15 . 3 .
- 10.1007/BF00967444 . Semiadjoint functors and Kan extensions . 1975 . Medvedev . M. Ya. . Siberian Mathematical Journal . 15 . 4 . 674–676 .
- Book: 10.1007/BFb0059148 . Set-Theoretical foundations of category theory . Reports of the Midwest Category Seminar III . Lecture Notes in Mathematics . 1969 . Feferman . Solomon . Kreisel . G. . 106 . 201–247 . 978-3-540-04625-7. 3.3. Case study of current category theory: specific illustrations. .
- Book: 10.1007/BFb0080770 . Foundations for categories and sets . Category Theory, Homology Theory and their Applications II . Lecture Notes in Mathematics . 1969 . Lane . Saunders Mac . 92 . 146–164 . 978-3-540-04611-0. V THE ADJOINT FUNCTOR THEOREM .
- Book: 10.1007/BFb0061361 . Abstract families and the adjoint functor theorems, ch. IV The adjoint functor theorems . [{{Google books|5X98CwAAQBAJ|page=94|plainurl=yes}} Indexed Categories and Their Applications ]. Lecture Notes in Mathematics . 1978 . Paré . Robert . Schumacher . Dietmar . 661 . 1–125 . 978-3-540-08914-8.
Further reading
External link