Abstract equations over signatures
Content created by Fernando Chu, Fredrik Bakke and Garrett Figueroa.
Created on 2023-03-20.
Last modified on 2025-09-05.
module universal-algebra.abstract-equations-over-signatures where
Imports
open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels open import universal-algebra.signatures open import universal-algebra.terms-over-signatures
Idea
An abstract equation over a signature σ
is a statement of a form “x
equals y
”, where x
and y
are terms over σ
. Thus, the data of an abstract
equation is simply two terms over a common signature.
Definitions
Abstract equations
module _ {l1 : Level} (σ : signature l1) where Abstract-Equation : UU l1 Abstract-Equation = Term σ × Term σ lhs-Abstract-Equation : Abstract-Equation → Term σ lhs-Abstract-Equation = pr1 rhs-Abstract-Equation : Abstract-Equation → Term σ rhs-Abstract-Equation = pr2
Recent changes
- 2025-09-05. Garrett Figueroa. Category of algebras of a theory (#1483).
- 2023-04-28. Fredrik Bakke. Miscellaneous refactoring and small additions (#579).
- 2023-03-20. Fernando Chu. Universal algebra first commit (#522).