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<html><head><meta charset="utf-8"><title>Categories.Category.Instance.One</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>
<a id="37" class="Keyword">open</a> <a id="42" class="Keyword">import</a> <a id="49" href="Level.html" class="Module">Level</a>
<a id="56" class="Keyword">module</a> <a id="63" href="Categories.Category.Instance.One.html" class="Module">Categories.Category.Instance.One</a> <a id="96" class="Keyword">where</a>
<a id="103" class="Keyword">open</a> <a id="108" class="Keyword">import</a> <a id="115" href="Data.Unit.html" class="Module">Data.Unit</a> <a id="125" class="Keyword">using</a> <a id="131" class="Symbol">(</a><a id="132" href="Agda.Builtin.Unit.html#175" class="Record">⊤</a><a id="133" class="Symbol">;</a> <a id="135" href="Agda.Builtin.Unit.html#212" class="InductiveConstructor">tt</a><a id="137" class="Symbol">)</a>
<a id="140" class="Keyword">open</a> <a id="145" class="Keyword">import</a> <a id="152" href="Categories.Category.html" class="Module">Categories.Category</a>
<a id="172" class="Keyword">open</a> <a id="177" class="Keyword">import</a> <a id="184" href="Categories.Functor.html" class="Module">Categories.Functor</a>
<a id="203" class="Keyword">open</a> <a id="208" class="Keyword">import</a> <a id="215" href="Categories.Category.Instance.Cats.html" class="Module">Categories.Category.Instance.Cats</a>
<a id="249" class="Keyword">import</a> <a id="256" href="Categories.Object.Terminal.html" class="Module">Categories.Object.Terminal</a> <a id="283" class="Symbol">as</a> <a id="286" class="Module">Term</a>
<a id="292" class="Keyword">module</a> <a id="299" href="Categories.Category.Instance.One.html#299" class="Module">_</a> <a id="301" class="Symbol">{</a><a id="302" href="Categories.Category.Instance.One.html#302" class="Bound">o</a> <a id="304" href="Categories.Category.Instance.One.html#304" class="Bound">ℓ</a> <a id="306" href="Categories.Category.Instance.One.html#306" class="Bound">e</a> <a id="308" class="Symbol">:</a> <a id="310" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="315" class="Symbol">}</a> <a id="317" class="Keyword">where</a>
<a id="325" class="Keyword">open</a> <a id="330" href="Categories.Object.Terminal.html" class="Module">Term</a> <a id="335" class="Symbol">(</a><a id="336" href="Categories.Category.Instance.Cats.html#628" class="Function">Cats</a> <a id="341" href="Categories.Category.Instance.One.html#302" class="Bound">o</a> <a id="343" href="Categories.Category.Instance.One.html#304" class="Bound">ℓ</a> <a id="345" href="Categories.Category.Instance.One.html#306" class="Bound">e</a><a id="346" class="Symbol">)</a>
<a id="351" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="355" class="Symbol">:</a> <a id="357" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="366" href="Categories.Category.Instance.One.html#302" class="Bound">o</a> <a id="368" href="Categories.Category.Instance.One.html#304" class="Bound">ℓ</a> <a id="370" href="Categories.Category.Instance.One.html#306" class="Bound">e</a>
<a id="374" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="378" class="Symbol">=</a> <a id="380" class="Keyword">record</a>
<a id="391" class="Symbol">{</a> <a id="393" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="403" class="Symbol">=</a> <a id="405" href="Level.html#409" class="Record">Lift</a> <a id="410" href="Categories.Category.Instance.One.html#302" class="Bound">o</a> <a id="412" href="Agda.Builtin.Unit.html#175" class="Record">⊤</a>
<a id="418" class="Symbol">;</a> <a id="420" href="Categories.Category.Core.html#575" class="Field Operator">_⇒_</a> <a id="430" class="Symbol">=</a> <a id="432" class="Symbol">λ</a> <a id="434" href="Categories.Category.Instance.One.html#434" class="Bound">_</a> <a id="436" href="Categories.Category.Instance.One.html#436" class="Bound">_</a> <a id="438" class="Symbol">→</a> <a id="440" href="Level.html#409" class="Record">Lift</a> <a id="445" href="Categories.Category.Instance.One.html#304" class="Bound">ℓ</a> <a id="447" href="Agda.Builtin.Unit.html#175" class="Record">⊤</a>
<a id="453" class="Symbol">;</a> <a id="455" href="Categories.Category.Core.html#595" class="Field Operator">_≈_</a> <a id="465" class="Symbol">=</a> <a id="467" class="Symbol">λ</a> <a id="469" href="Categories.Category.Instance.One.html#469" class="Bound">_</a> <a id="471" href="Categories.Category.Instance.One.html#471" class="Bound">_</a> <a id="473" class="Symbol">→</a> <a id="475" href="Level.html#409" class="Record">Lift</a> <a id="480" href="Categories.Category.Instance.One.html#306" class="Bound">e</a> <a id="482" href="Agda.Builtin.Unit.html#175" class="Record">⊤</a>
<a id="488" class="Symbol">}</a>
<a id="493" href="Categories.Category.Instance.One.html#493" class="Function">One-⊤</a> <a id="499" class="Symbol">:</a> <a id="501" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a>
<a id="512" href="Categories.Category.Instance.One.html#493" class="Function">One-⊤</a> <a id="518" class="Symbol">=</a> <a id="520" class="Keyword">record</a> <a id="527" class="Symbol">{</a> <a id="529" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="531" class="Symbol">=</a> <a id="533" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="537" class="Symbol">;</a> <a id="539" href="Categories.Object.Terminal.html#917" class="Field">⊤-is-terminal</a> <a id="553" class="Symbol">=</a> <a id="555" class="Keyword">record</a> <a id="562" class="Symbol">{</a> <a id="564" href="Categories.Object.Terminal.html#577" class="Field">!</a> <a id="566" class="Symbol">=</a> <a id="568" class="Keyword">record</a> <a id="575" class="Symbol">{</a> <a id="577" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="580" class="Symbol">=</a> <a id="582" class="Symbol">λ</a> <a id="584" href="Categories.Category.Instance.One.html#584" class="Bound">_</a> <a id="586" class="Symbol">→</a> <a id="588" href="Level.html#466" class="InductiveConstructor">lift</a> <a id="593" href="Agda.Builtin.Unit.html#212" class="InductiveConstructor">tt</a> <a id="596" class="Symbol">}</a> <a id="598" class="Symbol">}</a> <a id="600" class="Symbol">}</a>
<a id="603" class="Comment">-- not only is One terminal, it can be shifted anywhere else. Stronger version of !</a>
<a id="shift"></a><a id="687" href="Categories.Category.Instance.One.html#687" class="Function">shift</a> <a id="693" class="Symbol">:</a> <a id="695" class="Symbol">{</a><a id="696" href="Categories.Category.Instance.One.html#696" class="Bound">o</a> <a id="698" href="Categories.Category.Instance.One.html#698" class="Bound">ℓ</a> <a id="700" href="Categories.Category.Instance.One.html#700" class="Bound">e</a> <a id="702" class="Symbol">:</a> <a id="704" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="709" class="Symbol">}</a> <a id="711" class="Symbol">(</a><a id="712" href="Categories.Category.Instance.One.html#712" class="Bound">o′</a> <a id="715" href="Categories.Category.Instance.One.html#715" class="Bound">ℓ′</a> <a id="718" href="Categories.Category.Instance.One.html#718" class="Bound">e′</a> <a id="721" class="Symbol">:</a> <a id="723" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="728" class="Symbol">)</a> <a id="730" class="Symbol">→</a> <a id="732" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="740" class="Symbol">(</a><a id="741" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="745" class="Symbol">{</a><a id="746" href="Categories.Category.Instance.One.html#696" class="Bound">o</a><a id="747" class="Symbol">}</a> <a id="749" class="Symbol">{</a><a id="750" href="Categories.Category.Instance.One.html#698" class="Bound">ℓ</a><a id="751" class="Symbol">}</a> <a id="753" class="Symbol">{</a><a id="754" href="Categories.Category.Instance.One.html#700" class="Bound">e</a><a id="755" class="Symbol">})</a> <a id="758" class="Symbol">(</a><a id="759" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="763" class="Symbol">{</a><a id="764" href="Categories.Category.Instance.One.html#712" class="Bound">o′</a><a id="766" class="Symbol">}</a> <a id="768" class="Symbol">{</a><a id="769" href="Categories.Category.Instance.One.html#715" class="Bound">ℓ′</a><a id="771" class="Symbol">}</a> <a id="773" class="Symbol">{</a><a id="774" href="Categories.Category.Instance.One.html#718" class="Bound">e′</a><a id="776" class="Symbol">})</a>
<a id="779" href="Categories.Category.Instance.One.html#687" class="Function">shift</a> <a id="785" href="Categories.Category.Instance.One.html#785" class="Bound">o′</a> <a id="788" href="Categories.Category.Instance.One.html#788" class="Bound">ℓ′</a> <a id="791" href="Categories.Category.Instance.One.html#791" class="Bound">e′</a> <a id="794" class="Symbol">=</a> <a id="796" class="Symbol">_</a> <a id="798" class="Comment">-- so obvious, Agda can fill it all in automatically!</a>
<a id="One0"></a><a id="853" href="Categories.Category.Instance.One.html#853" class="Function">One0</a> <a id="858" class="Symbol">:</a> <a id="860" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="869" href="Level.html#521" class="Function">0ℓ</a> <a id="872" href="Level.html#521" class="Function">0ℓ</a> <a id="875" href="Level.html#521" class="Function">0ℓ</a>
<a id="878" href="Categories.Category.Instance.One.html#853" class="Function">One0</a> <a id="883" class="Symbol">=</a> <a id="885" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="889" class="Symbol">{</a><a id="890" href="Level.html#521" class="Function">0ℓ</a><a id="892" class="Symbol">}</a> <a id="894" class="Symbol">{</a><a id="895" href="Level.html#521" class="Function">0ℓ</a><a id="897" class="Symbol">}</a> <a id="899" class="Symbol">{</a><a id="900" href="Level.html#521" class="Function">0ℓ</a><a id="902" class="Symbol">}</a>
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