What does "Identity Types" mean?
Table of Contents
Identity types help us understand when two things are considered the same in a certain context. If we have two elements of the same type, identity types provide a way to show that they can be viewed as equal or identical.
Reflexive Graphs
A reflexive graph is a special structure that can represent identity types. It shows relationships between elements in a clear way. This structure helps organize the idea of equality, allowing us to work with complex systems more easily.
Reflexive Graph Lenses
Reflexive graph lenses are a new tool that simplifies the study of identity types. They sit between reflexive graphs and displayed reflexive graphs, making it easier to handle complicated cases. Each lens connects to a more complex displayed graph, enabling a clearer understanding of different structures.
Applications
These concepts have practical uses in various areas, such as group theory and type theory. By using reflexive graph lenses and understanding identity types, we can tackle complex problems with more confidence and clarity.