8
votes
2answers
201 views

Finding a functor satisfying a recursive equation

Say I want to find a functor satisfying something like: \[FA = 1 \sqcup (A \times FA).\] Equivalently, I want to find for each $A$ a fixed point of: \[GB = 1 \sqcup (A \times B)\] (I'll worry about ...
4
votes
2answers
263 views

Fixed points in category theory

Is there a usual way to express the concept of fixed points in category theory? What would I say to express that a morphism has a fixed point? Thank you!