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felixwellen committed Jun 19, 2024
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508 changes: 249 additions & 259 deletions Cubical.Algebra.Group.GroupPath.html

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2 changes: 1 addition & 1 deletion Cubical.Algebra.Group.Instances.Unit.html
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<a id="isContr→≡UnitGroup"></a><a id="3045" href="Cubical.Algebra.Group.Instances.Unit.html#3045" class="Function">isContr→≡UnitGroup</a> <a id="3064" class="Symbol">:</a> <a id="3066" class="Symbol">{</a><a id="3067" href="Cubical.Algebra.Group.Instances.Unit.html#3067" class="Bound">G</a> <a id="3069" class="Symbol">:</a> <a id="3071" href="Cubical.Algebra.Group.Base.html#1230" class="Function">Group</a> <a id="3077" href="Agda.Primitive.html#915" class="Primitive">ℓ-zero</a><a id="3083" class="Symbol">}</a> <a id="3085" class="Symbol"></a> <a id="3087" href="Cubical.Foundations.Prelude.html#15052" class="Function">isContr</a> <a id="3095" class="Symbol">(</a><a id="3096" href="Agda.Builtin.Sigma.html#251" class="Field">fst</a> <a id="3100" href="Cubical.Algebra.Group.Instances.Unit.html#3067" class="Bound">G</a><a id="3101" class="Symbol">)</a> <a id="3103" class="Symbol"></a> <a id="3105" href="Cubical.Algebra.Group.Instances.Unit.html#599" class="Function">UnitGroup₀</a> <a id="3116" href="Agda.Builtin.Cubical.Path.html#272" class="Function Operator"></a> <a id="3118" href="Cubical.Algebra.Group.Instances.Unit.html#3067" class="Bound">G</a>
<a id="3120" href="Cubical.Algebra.Group.Instances.Unit.html#3045" class="Function">isContr→≡UnitGroup</a> <a id="3139" href="Cubical.Algebra.Group.Instances.Unit.html#3139" class="Bound">c</a> <a id="3141" class="Symbol">=</a>
<a id="3145" href="Agda.Builtin.Sigma.html#251" class="Field">fst</a> <a id="3149" class="Symbol">(</a><a id="3150" href="Cubical.Algebra.Group.GroupPath.html#1402" class="Function">GroupPath</a> <a id="3160" class="Symbol">_</a> <a id="3162" class="Symbol">_)</a>
<a id="3145" href="Agda.Builtin.Sigma.html#251" class="Field">fst</a> <a id="3149" class="Symbol">(</a><a id="3150" href="Cubical.Algebra.Group.GroupPath.html#1443" class="Function">GroupPath</a> <a id="3160" class="Symbol">_</a> <a id="3162" class="Symbol">_)</a>
<a id="3169" class="Symbol">(</a><a id="3170" href="Cubical.Algebra.Group.MorphismProperties.html#8392" class="Function">invGroupEquiv</a> <a id="3184" class="Symbol">((</a><a id="3186" href="Cubical.Data.Unit.Properties.html#2419" class="Function">isContr→≃Unit</a> <a id="3200" href="Cubical.Algebra.Group.Instances.Unit.html#3139" class="Bound">c</a><a id="3201" class="Symbol">)</a>
<a id="3221" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="3223" class="Symbol">(</a><a id="3224" href="Cubical.Algebra.Group.MorphismProperties.html#2406" class="Function">makeIsGroupHom</a> <a id="3239" class="Symbol"></a> <a id="3242" href="Cubical.Algebra.Group.Instances.Unit.html#3242" class="Bound">_</a> <a id="3244" href="Cubical.Algebra.Group.Instances.Unit.html#3244" class="Bound">_</a> <a id="3246" class="Symbol"></a> <a id="3248" href="Cubical.Foundations.Prelude.html#915" class="Function">refl</a><a id="3252" class="Symbol">))))</a>

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2 changes: 1 addition & 1 deletion Cubical.Algebra.Group.IsomorphismTheorems.html
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<a id="4024" class="Comment">-- The SIP lets us turn the isomorphism theorem into a path</a>
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<a id="4127" href="Cubical.Algebra.Group.IsomorphismTheorems.html#4086" class="Function">pathThm1</a> <a id="4136" class="Symbol">=</a> <a id="4138" href="Cubical.Algebra.Group.GroupPath.html#4286" class="Function">uaGroup</a> <a id="4146" class="Symbol">(</a><a id="4147" href="Cubical.Algebra.Group.MorphismProperties.html#10885" class="Function">GroupIso→GroupEquiv</a> <a id="4167" href="Cubical.Algebra.Group.IsomorphismTheorems.html#3823" class="Function">isoThm1</a><a id="4174" class="Symbol">)</a>
<a id="4127" href="Cubical.Algebra.Group.IsomorphismTheorems.html#4086" class="Function">pathThm1</a> <a id="4136" class="Symbol">=</a> <a id="4138" href="Cubical.Algebra.Group.GroupPath.html#4327" class="Function">uaGroup</a> <a id="4146" class="Symbol">(</a><a id="4147" href="Cubical.Algebra.Group.MorphismProperties.html#10885" class="Function">GroupIso→GroupEquiv</a> <a id="4167" href="Cubical.Algebra.Group.IsomorphismTheorems.html#3823" class="Function">isoThm1</a><a id="4174" class="Symbol">)</a>

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<a id="4225" href="Cubical.Algebra.Group.IsomorphismTheorems.html#4179" class="Function">surjImIso</a> <a id="4235" href="Cubical.Algebra.Group.IsomorphismTheorems.html#4235" class="Bound">surj</a> <a id="4240" class="Symbol">=</a>
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