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<ahref='https://anders.groupoid.space/mathematics/analysis/octo/'>𝕆</a></li></ol></div><divclass="macro__col"><h3id="algebra"><b>ALGEBRA</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/algebra/group/">GROUP</a></li><li><ahref="https://anders.groupoid.space/mathematics/algebra/algebra/">ALGEBRA</a></li><li><ahref="https://anders.groupoid.space/mathematics/algebra/homology/">HOMOLOGY</a></li></ol></div><divclass="macro__col"><h3id="geometry"><b>GEOMETRY</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/geometry/etale/">ETALE</a></li><li><ahref="https://anders.groupoid.space/mathematics/geometry/bundle/">BUNDLE</a></li><li><ahref="https://anders.groupoid.space/mathematics/geometry/manifold/">MANIFOLD</a></li><li><ahref="https://anders.groupoid.space/mathematics/geometry/derham/">DE RHAM</a></li></ol></div><divclass="macro__col"><h3id="homotopy"><b>HOMOTOPY</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/homotopy/coequalizer/">COEQUALIZER</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/pushout/">PUSHOUT</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/pullback/">PULLBACK</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/hopf/">HOPF</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/cw/">CW</a></li></ol></div></div></section><section><divclass="macro"><divclass="macro__col"><h3id="categories"><b>CATEGORIES</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/categories/category/">CATEGORY</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/functor/">FUNCTOR</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/groupoid/">GROUPOID</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/topos/">TOPOS</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/presheaf/">PRESHEAF</a></li></ol></div></div></section><br><p>The base library for <b>cubicaltt</b> is given on separate page:
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<ahref='https://anders.groupoid.space/mathematics/analysis/octo/'>𝕆</a></li></ol></div><divclass="macro__col"><h3id="algebra"><b>ALGEBRA</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/algebra/group/">GROUP</a></li><li><ahref="https://anders.groupoid.space/mathematics/algebra/algebra/">ALGEBRA</a></li><li><ahref="https://anders.groupoid.space/mathematics/algebra/homology/">HOMOLOGY</a></li></ol></div><divclass="macro__col"><h3id="geometry"><b>GEOMETRY</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/geometry/etale/">ETALE</a></li><li><ahref="https://anders.groupoid.space/mathematics/geometry/bundle/">BUNDLE</a></li><li><ahref="https://anders.groupoid.space/mathematics/geometry/manifold/">MANIFOLD</a></li><li><ahref="https://anders.groupoid.space/mathematics/geometry/derham/">DE RHAM</a></li></ol></div></div></section><section><divclass="macro"><divclass="macro__col"><h3id="homotopy"><b>HOMOTOPY</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/homotopy/coequalizer/">COEQUALIZER</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/pushout/">PUSHOUT</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/pullback/">PULLBACK</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/hopf/">HOPF</a></li><li><ahref="https://anders.groupoid.space/mathematics/homotopy/cw/">CW</a></li></ol></div><divclass="macro__col"><h3id="categories"><b>CATEGORIES</b></h3><ol><li><ahref="https://anders.groupoid.space/mathematics/categories/category/">CATEGORY</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/functor/">FUNCTOR</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/groupoid/">GROUPOID</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/topos/">TOPOS</a></li><li><ahref="https://anders.groupoid.space/mathematics/categories/presheaf/">PRESHEAF</a></li></ol></div></div></section><br><p>The base library for <b>cubicaltt</b> is given on separate page:
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<ahref='https://groupoid.space/misc/library/'>Formal Mathematics: The Cubical Base Library</a><br>
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</p><h1>Languages</h1><p>Non-dependent languages are targets or runtimes, and dependently typed language are provers.
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</p><h2>Verification</h2><p>Theorem provers for logic, lambda encodings exploration and homotopy calculus.</p><p>05 APR 2022 — <ahref='https://alonzo.groupoid.space/'>Alonzo: STLC</a><br>
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