<p>When modelling an architecture in UML component diagrams, how do you show various attributes of connectors simultaneously? Like </p>

<ul>
<li>business object information flow (A->B, B->A, A&lt;->B)</li>
<li>request/response direction</li>
<li>synchronous/asynchronous behaviour</li>
</ul>

<p>I am aware of other diagram types like sequence diagrams. However, having this information visible in component diagrams would have value. </p>

<p>What is possible beyond associations (merely showing that components are connected) or "lollipops" (request/response)?</p>

You might want to use
sequence diagrams
instead of class (i.e, component) diagrams.
If you want to stick to a static diagram, you may also want to consider adding << sterotypes>> to various connectors, or even use
association classes
.
If possible, you can use connectors from sequence diagrams to connect classifiers in component diagrams (e.g., synchronous/asynchronous message-passing arrows).