Categories with negation

Jaiung Jun, Louis Rowen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We continue the theory of T-systems from the work of the second author, describing both ground systems and systemic modules over a ground system (paralleling the theory of modules over an algebra). The theory, summarized categorically at the end, encapsulates general algebraic structures lacking negation but possessing a map resembling negation, such as tropical algebras, hyperfields and fuzzy rings. We see explicitly how it encompasses tropical algebraic theory and hyperfields.

Original languageEnglish
Pages (from-to)221-270
Number of pages50
JournalContemporary Mathematics
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society.


  • Algebraic
  • Bipotent
  • Category
  • Congruence
  • Congruence
  • Dimension
  • Hyperfield
  • Hypergroup
  • Matroid
  • Meta-tangible
  • Module
  • Negation
  • Polynomial
  • Prime
  • Pseudo-system
  • Pseudo-triple
  • Semifield
  • Semiring
  • Supertropical algebra
  • Surpassing relation
  • Symmetrization
  • Symmetrized
  • System
  • Tensor product
  • Triple
  • Tropical algebra


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