categorification

A procedure that defines theorems in terms of category theory by mapping concepts from set theory to category theory.

Noun

  1. A procedure that defines theorems in terms of category theory by mapping concepts from set theory to category theory.
    • 2008, E. Krenkel, Ramifications of the Geometric Langlands Program, Michael Cowling, Edward Frenkel, Masaki Kashiwara, Alain Valette, David A. Vogan, Jr., Nolan R. Wallach (editors), Representation Theory and Complex...
    • 2009, Volodymyr Mazorchuk, Lectures on sl₂( C )-Modules, Imperial College Press, page 221, Show that Φ⊕Φ is also a (naïve) homomorphism of naïve categorifications.
    • Khovanov's categorification of the Jones polynomial by Khovanov homology is the subject of Section 11.6. - 2010, Kishore Marathe, Topics in Physical Mathematics, Springer, page 351:

Origin

From category + -fication.

Forms

categorifications

Derived

decategorification horizontal categorification vertical categorification