# nLab Morita morphism

∞-Lie theory

## Examples

### $\infty$-Lie algebras

The most useful notion of homomorphism between Lie groupoids is not that of a functor internal to the category SmoothMfd of smooth manifolds (even though Lie groupoids can be regarded as internal groupoids in SmoothMfd), but is that of a morphism of smooth stacks (differentiable stacks) on the site SmoothMfd. To amplify this distinction in the literature a wealth of names and terms for these non-naïve homomorphisms is used, such as Morita morphism . In particular a Morita morphism which is a homotopy equivalence is a Morita equivalence.

Ways to present the correct notion of homomorphism include

Revised on March 2, 2014 11:38:53 by Coward Anonymous? (93.147.79.110)