Homotopy Type Theory Algebra > history (Rev #24)

Here we collect articles about doing set-level algebra in HoTT.

Decidable objects

• booleans
• decidable universal quantifier
• decidable existential quantifier
• decidable directed graph
• decidable setoid
• decidable set
• decidable preordered type
• decidable strict order
• decidable dense strict order?

Inverse images

• inverse image
• iterated inverse image
• infinitely iterated inverse image

Images

• axiom of replacement

Rings, modules, and algebras

• abelian group/Z-module
• divisible group
• torsion-free divisible group/Q-module
• halving group/D-module
• abelian group homomorphism
• bilinear function
• ring
• commutative ring
• algebra (ring theory)
• Q-algebra
• commutative algebra (ring theory)
• polynomial ring
• univariate polynomial ring

Sequences

• sequence
• left shift operator
• right shift operator
• Z-module
• sequential polynomial
• series operator
• inverse series operator
• sequential derivative
• Q-vector space
• sequential antiderivative

Relations

• binary relation
• functional relation
• entire relation
• apartness relation
• order
• strict order

Ordered commutative rings

• ordered integral domain
• Archimedean ordered integral domain
• ordered field
• Archimedean ordered field
• sequentially Cauchy complete Archimedean ordered field

References

• HoTT Book
• Henri Lombardi, Claude Quitté, Commutative algebra: Constructive methods. Finite projective modules, arXiv:1605.04832