https://wiki.lojban.io/index.php?action=history&feed=atom&title=facni 2026-04-28T00:21:15Z Revision history for this page on the wiki MediaWiki 1.45.3 https://wiki.lojban.io/index.php?title=facni&diff=4797&oldid=prev 2026-01-13T14:51:55Z

<p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> facni<br /> ==== type ====<br /> experimental gismu<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Wed Feb 22 20:13:45 2017<br />  <br /> == English ==<br /> === Definition #69387 - Preferred ===<br />  <br /> ==== definition ====<br /> x&lt;sub&gt;1&lt;/sub&gt; is an n-ary operator/map which is distributive/linear/homomorphic in or over or from space/structure x&lt;sub&gt;2&lt;/sub&gt;, mapping to space or structure x&lt;sub&gt;3&lt;/sub&gt;, thereby producing a new space/structure x&lt;sub&gt;4&lt;/sub&gt; which is the &#039;union&#039; of x&lt;sub&gt;2&lt;/sub&gt; and x&lt;sub&gt;3&lt;/sub&gt; endowed with x&lt;sub&gt;1&lt;/sub&gt;; x&lt;sub&gt;1&lt;/sub&gt; distributes over/through all of the operators of x&lt;sub&gt;2&lt;/sub&gt;. <br /> ==== notes ====<br /> x&lt;sub&gt;2&lt;/sub&gt; and x&lt;sub&gt;3&lt;/sub&gt; cannot merely be sets; they must be structures/systems which each are a set/category endowed with at least one operator/relation/property (here, &quot;operator&quot; will refer to any of these options) each; the ith operator endowing one space corresponds to exactly the ith operator endowing the other space under mapping x&lt;sub&gt;1&lt;/sub&gt;. For any operator of x&lt;sub&gt;2&lt;/sub&gt;, x&lt;sub&gt;1&lt;/sub&gt; is commutative with it with respect to functional composition ([[fa&#039;ai|fa&#039;ai]]) when the (other) operator is &#039;translated&#039; to the corresponding operator of x&lt;sub&gt;3&lt;/sub&gt; appropriately. x&lt;sub&gt;1&lt;/sub&gt; is linear/a linear operator; x&lt;sub&gt;1&lt;/sub&gt; is a homomorphism; x&lt;sub&gt;1&lt;/sub&gt; distributes. x&lt;sub&gt;2&lt;/sub&gt; is homomorphic with x&lt;sub&gt;3&lt;/sub&gt; under x&lt;sub&gt;1&lt;/sub&gt;; they need not be identical (in fact, their respective operators need not even be identical, just &#039;homomorphically similar&#039;). For &quot;distributivity&quot;/&quot;distributive property&quot;, &quot;linearity of operator&quot;, or &quot;homomorphicity of operator&quot;, use &quot;ka(m)( )facni&quot; with x&lt;sub&gt;1&lt;/sub&gt; filled with &quot;[[ce&#039;u|ce&#039;u]]&quot;; for &quot;homomorphicity of spaces&quot;, use the same thing, but with x&lt;sub&gt;2&lt;/sub&gt; or x&lt;sub&gt;3&lt;/sub&gt; filled with &quot;[[ce&#039;u|ce&#039;u]]&quot;. See also: &quot;[[socni|socni]]&quot;, &quot;[[cajni|cajni]]&quot;, &quot;[[sezni|sezni]]&quot;, &quot;[[dukni|dukni]]&quot;; &quot;[[fa&#039;ai|fa&#039;ai]]&quot;; &quot;[[fatri|fatri]]&quot;. This is a structure-operator-preserving function, and thus is an example of a [[stodraunju|stodraunju]].<br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/distributive function|distributive function]]&lt;/li&gt;&lt;li&gt;[[natlang/en/distributive operator|distributive operator]]&lt;/li&gt;&lt;li&gt;[[natlang/en/distributive property|distributive property]]&lt;/li&gt;&lt;li&gt;[[natlang/en/graph homomorphism|graph homomorphism]]&lt;/li&gt;&lt;li&gt;[[natlang/en/homomorphicity|homomorphicity]]&lt;/li&gt;&lt;li&gt;[[natlang/en/homomorphism|homomorphism ; algebra]]&lt;/li&gt;&lt;li&gt;[[natlang/en/linear function|linear function ; linear algebra]]&lt;/li&gt;&lt;li&gt;[[natlang/en/linear map|linear map ; vector space homomorphism]]&lt;/li&gt;&lt;li&gt;[[natlang/en/linear operator|linear operator]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Fri Aug 12 17:55:36 2022<br /> <br /> <br /> <br /> &lt;br/&gt;&lt;font size=&quot;+1&quot;&gt;Examples&lt;/font&gt;<br /> &lt;hr/&gt;<br /> &lt;dl&gt;<br /> &lt;/dl&gt;<br /> <br /> === Etymology ===</div>

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