# nLab Morita morphism

### Context

#### $\infty$-Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Related topics

Examples

$\infty$-Lie groupoids

$\infty$-Lie groups

$\infty$-Lie algebroids

$\infty$-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

Last revised on November 2, 2021 at 09:38:34. See the history of this page for a list of all contributions to it.