[DSRP Evidence](https://dsrpevidence.org/)

# Every object has an identity morphism

Mereology & mathematics · 

## Why it looked like it would break the theory

In category theory, every object has an identity morphism, id_A: A → A. This appears to challenge the Relationship pattern because the source and target are the same identity rather than two distinct identities.

## Why it failed

**The counterexample failed** because DSRP does not require a relationship to connect different identities. Any identity may relate to any identity, including itself: i_x ↔R i_x. An identity morphism is therefore an ordinary self-relationship. The source and target instantiate the same identity, but the Relationship structure remains present.

Settled by [R10](https://dsrpevidence.org/resolution/10). Not yet published.

[Read it](https://plato.stanford.edu/entries/category-theory/)

[All cases](https://dsrpevidence.org/counterexamples)