Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
An equivalence relation on an algebra that is preserved by every basic operation, so applying an operation to pairwise equivalent inputs gives equivalent outputs.
burris-universal-algebraEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A congruence identifies elements only when every basic operation respects the identification, which is the condition needed for operations to descend to equivalence classes.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
burris-universal-algebraEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Congruence compatibility is precisely what makes the value of every induced operation independent of the selected representatives of its input classes.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
burris-universal-algebra