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alectryon-html/HoTT.Algebra.AbGroups.Abelianization.html
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| <pre class="alectryon-io"><!-- Generator: Alectryon --><span class="alectryon-wsp"><span class="highlight"><span class="sd">(** Theory *)</span> | ||
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| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.Groups.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-wsp"><span class="highlight"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.AbelianGroup.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.Abelianization.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.AbPullback.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.AbPushout.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.Biproduct.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.AbHom.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.Cyclic.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.Centralizer.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-wsp"><span class="highlight"> | ||
| <span class="c">(* The theory of Ext groups of abelian groups is in HoTT.Algebra.AbSES. *)</span> | ||
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| <span class="sd">(** Examples *)</span> | ||
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| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> HoTT.Algebra.AbGroups.Z.</span></span></span></pre> | ||
| </div> | ||
| </div></body> | ||
| </html> |
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alectryon-html/HoTT.Algebra.AbSES.PullbackFiberSequence.html
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| <div class="alectryon-root alectryon-centered"><div class="alectryon-banner">Built with <a href="https://github.com/cpitclaudel/alectryon/">Alectryon</a>, running Coq+SerAPI v8.16.0+0.16.3. Bubbles (<span class="alectryon-bubble"></span>) indicate interactive fragments: hover for details, tap to reveal contents. Use <kbd>Ctrl+↑</kbd> <kbd>Ctrl+↓</kbd> to navigate, <kbd>Ctrl+🖱️</kbd> to focus. On Mac, use <kbd>⌘</kbd> instead of <kbd>Ctrl</kbd>.</div><div class="document"> | ||
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| <pre class="alectryon-io"><!-- Generator: Alectryon --><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.Core.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.Ext.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.Pullback.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.PullbackFiberSequence.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.Pushout.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.BaerSum.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.DirectSum.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Export</span> AbSES.SixTerm.</span></span></span></pre> | ||
| </div> | ||
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| <title>Aut.v</title> | ||
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| <meta name="viewport" content="width=device-width, initial-scale=1"> | ||
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| <div class="alectryon-root alectryon-centered"><div class="alectryon-banner">Built with <a href="https://github.com/cpitclaudel/alectryon/">Alectryon</a>, running Coq+SerAPI v8.16.0+0.16.3. Bubbles (<span class="alectryon-bubble"></span>) indicate interactive fragments: hover for details, tap to reveal contents. Use <kbd>Ctrl+↑</kbd> <kbd>Ctrl+↓</kbd> to navigate, <kbd>Ctrl+🖱️</kbd> to focus. On Mac, use <kbd>⌘</kbd> instead of <kbd>Ctrl</kbd>.</div><div class="document"> | ||
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| <pre class="alectryon-io"><!-- Generator: Alectryon --><span class="alectryon-wsp"><span class="highlight"><span class="c">(* -*- mode: coq; mode: visual-line -*- *)</span> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Import</span> Basics.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Import</span> Truncations.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Import</span> Algebra.ooGroup.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Import</span> Spaces.BAut.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Import</span> Pointed.Core.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-wsp"><span class="highlight"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Local Open Scope</span> pointed_scope.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-wsp"><span class="highlight"> | ||
| <span class="sd">(** * Automorphism oo-Groups *)</span> | ||
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| <span class="sd">(** We define [Aut X] using the pointed, connected type [BAut X]. *)</span> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">Aut</span> (<span class="nv">X</span> : <span class="kt">Type</span>) : ooGroup | ||
| := Build_ooGroup [BAut X, _] _.</span></span></span></pre> | ||
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| <div class="alectryon-root alectryon-centered"><div class="alectryon-banner">Built with <a href="https://github.com/cpitclaudel/alectryon/">Alectryon</a>, running Coq+SerAPI v8.16.0+0.16.3. Bubbles (<span class="alectryon-bubble"></span>) indicate interactive fragments: hover for details, tap to reveal contents. Use <kbd>Ctrl+↑</kbd> <kbd>Ctrl+↓</kbd> to navigate, <kbd>Ctrl+🖱️</kbd> to focus. On Mac, use <kbd>⌘</kbd> instead of <kbd>Ctrl</kbd>.</div><div class="document"> | ||
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| <pre class="alectryon-io"><!-- Generator: Alectryon --><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Require Import</span> Classes.interfaces.abstract_algebra.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-wsp"><span class="highlight"> | ||
| <span class="c">(* We say that a relation is a congruence if it respects the operation.</span> | ||
| <span class="c"> This is technically incorrect since we are not enforcing the relation to be an equivalence relation.</span> | ||
| <span class="c">*)</span> | ||
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| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Local Open Scope</span> mc_mult_scope.</span></span><span class="alectryon-wsp"> | ||
| </span></span><span class="alectryon-wsp"><span class="highlight"> | ||
| </span></span><span class="alectryon-sentence"><span class="alectryon-input"><span class="highlight"><span class="kn">Class</span> <span class="nf">IsCongruence</span> {<span class="nv">G</span>} `{SgOp G} (R : Relation G) := { | ||
| iscong {x x' y y'} : R x x' -> R y y' -> R (x * y) (x' * y'); | ||
| }.</span></span></span></pre> | ||
| </div> | ||
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