category of Jónsson-Tarski algebras

 algebra  set theory
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 M−SetM{-}\Set External nLab Link

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

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

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: surjective morphisms

Indistinguishable categories

These categories in the database currently have exactly the same properties as the category of Jónsson-Tarski algebras. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.