<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On 7 Oct 2011, at 05:30, Dan Doel wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; ">Induction-recursion is not (from what I've read) justified by functors<br>over the category of types, but by functors over a related category.<br>But their actions are supposed to be strictly positive there, I<br>believe.</span></blockquote></div><br><div>Do you mean that IR defs are containers in Fam(D)?</div><div><br></div><div>I don't think this is the case. If I remember correctly containers in Fam(D)</div><div>give rise to functors where the first component (e.g. U : D) does not depend</div><div>on the 2nd (eg T : U -> Set).</div><div><br></div><div>Thorsten</div></body></html>