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32 lines
7.6 KiB
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<html><head><meta charset="utf-8"><title>Categories.Category.Instance.SingletonSet</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
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<a id="37" class="Keyword">open</a> <a id="42" class="Keyword">import</a> <a id="49" href="Level.html" class="Module">Level</a>
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<a id="56" class="Comment">-- This is really a degenerate version of Categories.Category.Instance.One</a>
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<a id="131" class="Comment">-- Here SingletonSet is not given an explicit name, it is an alias for ⊤</a>
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<a id="204" class="Keyword">module</a> <a id="211" href="Categories.Category.Instance.SingletonSet.html" class="Module">Categories.Category.Instance.SingletonSet</a> <a id="253" class="Keyword">where</a>
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<a id="260" class="Keyword">open</a> <a id="265" class="Keyword">import</a> <a id="272" href="Data.Unit.Polymorphic.html" class="Module">Data.Unit.Polymorphic</a> <a id="294" class="Keyword">using</a> <a id="300" class="Symbol">(</a><a id="301" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a><a id="302" class="Symbol">;</a> <a id="304" href="Data.Unit.Polymorphic.Base.html#533" class="Function">tt</a><a id="306" class="Symbol">)</a>
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<a id="308" class="Keyword">open</a> <a id="313" class="Keyword">import</a> <a id="320" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="336" class="Keyword">using</a> <a id="342" class="Symbol">(</a><a id="343" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="349" class="Symbol">)</a>
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<a id="351" class="Keyword">open</a> <a id="356" class="Keyword">import</a> <a id="363" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a> <a id="401" class="Keyword">using</a> <a id="407" class="Symbol">(</a><a id="408" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a><a id="412" class="Symbol">)</a>
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<a id="415" class="Keyword">open</a> <a id="420" class="Keyword">import</a> <a id="427" href="Categories.Category.Instance.Sets.html" class="Module">Categories.Category.Instance.Sets</a>
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<a id="461" class="Keyword">open</a> <a id="466" class="Keyword">import</a> <a id="473" href="Categories.Category.Instance.Setoids.html" class="Module">Categories.Category.Instance.Setoids</a>
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<a id="510" class="Keyword">import</a> <a id="517" href="Categories.Object.Terminal.html" class="Module">Categories.Object.Terminal</a> <a id="544" class="Symbol">as</a> <a id="547" class="Module">Term</a>
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<a id="553" class="Keyword">module</a> <a id="560" href="Categories.Category.Instance.SingletonSet.html#560" class="Module">_</a> <a id="562" class="Symbol">{</a><a id="563" href="Categories.Category.Instance.SingletonSet.html#563" class="Bound">o</a> <a id="565" class="Symbol">:</a> <a id="567" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="572" class="Symbol">}</a> <a id="574" class="Keyword">where</a>
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<a id="582" class="Keyword">open</a> <a id="587" href="Categories.Object.Terminal.html" class="Module">Term</a> <a id="592" class="Symbol">(</a><a id="593" href="Categories.Category.Instance.Sets.html#416" class="Function">Sets</a> <a id="598" href="Categories.Category.Instance.SingletonSet.html#563" class="Bound">o</a><a id="599" class="Symbol">)</a>
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<a id="604" href="Categories.Category.Instance.SingletonSet.html#604" class="Function">SingletonSet-⊤</a> <a id="619" class="Symbol">:</a> <a id="621" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a>
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<a id="632" href="Categories.Category.Instance.SingletonSet.html#604" class="Function">SingletonSet-⊤</a> <a id="647" class="Symbol">=</a> <a id="649" class="Keyword">record</a> <a id="656" class="Symbol">{</a> <a id="658" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="660" class="Symbol">=</a> <a id="662" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="664" class="Symbol">;</a> <a id="666" href="Categories.Object.Terminal.html#917" class="Field">⊤-is-terminal</a> <a id="680" class="Symbol">=</a> <a id="682" class="Keyword">record</a> <a id="689" class="Symbol">{</a> <a id="691" href="Categories.Object.Terminal.html#605" class="Field">!-unique</a> <a id="700" class="Symbol">=</a> <a id="702" class="Symbol">λ</a> <a id="704" href="Categories.Category.Instance.SingletonSet.html#704" class="Bound">_</a> <a id="706" class="Symbol">→</a> <a id="708" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a> <a id="713" class="Symbol">}</a> <a id="715" class="Symbol">}</a>
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<a id="718" class="Keyword">module</a> <a id="725" href="Categories.Category.Instance.SingletonSet.html#725" class="Module">_</a> <a id="727" class="Symbol">{</a><a id="728" href="Categories.Category.Instance.SingletonSet.html#728" class="Bound">c</a> <a id="730" href="Categories.Category.Instance.SingletonSet.html#730" class="Bound">ℓ</a> <a id="732" class="Symbol">:</a> <a id="734" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="739" class="Symbol">}</a> <a id="741" class="Keyword">where</a>
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<a id="749" class="Keyword">open</a> <a id="754" href="Categories.Object.Terminal.html" class="Module">Term</a> <a id="759" class="Symbol">(</a><a id="760" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="768" href="Categories.Category.Instance.SingletonSet.html#728" class="Bound">c</a> <a id="770" href="Categories.Category.Instance.SingletonSet.html#730" class="Bound">ℓ</a><a id="771" class="Symbol">)</a>
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<a id="776" href="Categories.Category.Instance.SingletonSet.html#776" class="Function">SingletonSetoid</a> <a id="792" class="Symbol">:</a> <a id="794" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="801" href="Categories.Category.Instance.SingletonSet.html#728" class="Bound">c</a> <a id="803" href="Categories.Category.Instance.SingletonSet.html#730" class="Bound">ℓ</a>
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<a id="807" href="Categories.Category.Instance.SingletonSet.html#776" class="Function">SingletonSetoid</a> <a id="823" class="Symbol">=</a> <a id="825" class="Keyword">record</a> <a id="832" class="Symbol">{</a> <a id="834" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="842" class="Symbol">=</a> <a id="844" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="846" class="Symbol">;</a> <a id="848" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a> <a id="852" class="Symbol">=</a> <a id="854" class="Symbol">λ</a> <a id="856" href="Categories.Category.Instance.SingletonSet.html#856" class="Bound">_</a> <a id="858" href="Categories.Category.Instance.SingletonSet.html#858" class="Bound">_</a> <a id="860" class="Symbol">→</a> <a id="862" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="864" class="Symbol">}</a>
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<a id="869" href="Categories.Category.Instance.SingletonSet.html#869" class="Function">SingletonSetoid-⊤</a> <a id="887" class="Symbol">:</a> <a id="889" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a>
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<a id="900" href="Categories.Category.Instance.SingletonSet.html#869" class="Function">SingletonSetoid-⊤</a> <a id="918" class="Symbol">=</a> <a id="920" class="Keyword">record</a> <a id="927" class="Symbol">{</a> <a id="929" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="931" class="Symbol">=</a> <a id="933" href="Categories.Category.Instance.SingletonSet.html#776" class="Function">SingletonSetoid</a> <a id="949" class="Symbol">}</a>
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</pre></body></html>
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