Metamath Proof Explorer


Table of Contents - 21.20.6.4. Direct image and inverse image

Definitions of the functionalized direct image and inverse image.

The functionalized direct (resp. inverse) image is the morphism component of the covariant (resp. contravariant) powerset endofunctor of the category of sets and relations (and, up to restriction, of its subcategory of sets and functions). Its object component is the powerset operation defined in df-pw.

  1. cimdir
  2. df-imdir
  3. bj-imdirvallem
  4. bj-imdirval
  5. bj-imdirval2lem
  6. bj-imdirval2
  7. bj-imdirval3
  8. bj-imdiridlem
  9. bj-imdirid
  10. bj-opelopabid
  11. bj-opabco
  12. bj-xpcossxp
  13. bj-imdirco
  14. ciminv
  15. df-iminv
  16. bj-iminvval
  17. bj-iminvval2
  18. bj-iminvid