category of Jónsson-Tarski algebras

  • notation: J2\J_2
  • objects: pairs (X,α)(X,\alpha), where XX is a set and α:X→X×X\alpha : X \to X \times X is an isomorphism
  • morphisms: A morphism (X,α)→(Y,β)(X,\alpha) \to (Y,\beta) is a map f:X→Yf : X \to Y satisfying (f×f)∘α=β∘f.(f \times f) \circ \alpha = \beta \circ f.
  • Related categories: M−SetM{-}\Set
  • nLab Link

This is interesting example of a category in the intersection of topos theory and algebra.

Satisfied Properties

Properties from the database

Deduced properties

Unsatisfied Properties

Properties from the database

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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Special objects

  • terminal object: ({∗},!)(\{\ast\},!)
  • initial object: (∅,!)(\varnothing,!)
  • products: direct products with pointwise operations
  • coproducts: See here for a description

Special morphisms

  • isomorphisms: bijective morphisms
  • monomorphisms: injective morphisms
  • epimorphisms: surjective morphisms
  • regular monomorphisms: same as monomorphisms
  • regular epimorphisms: same as epimorphisms