volume 4 articles

Author: 5HT

books/vol4/id.pdf

@@ -26,7 +26,7 @@
 <a href='https://groupoid.space/misc/library/'>Formal Mathematics: The Cubical Base Library</a><br>
 
 </p></div><div class="exe"><section></section><h1>ARTICLES</h1><p>Then we publish this as an article for peer review and include in
-series of articles on foundation and mathematics of Homotopy Type Theory.</p><br><br></div><div class="types"><div class="type"><ol class="type__col"><h3>Foundations</h3><li style="font-size:14px;"><a href="https://groupoid.space/articles/mltt/mltt.pdf">Type Theory</a></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/cic/cic.pdf">Inductive Types</a></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/hott/hott.pdf">Homotopy Type Theory</a></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/hit/hit.pdf">Higher Inductive Types</a></li><li style="font-size:14px;"><b>Modalities</b></li></ol><ol class="type__col"><h3>Languages</h3><li style="font-size:14px;"><a href="https://groupoid.space/articles/laurent/laurent.pdf">Laurent Schwartz</a></li><li style="font-size:14px;"><b>Ernst Zermelo</b></li><li style="font-size:14px;"><b>Paul Cohen</b></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/henk/henk.pdf">Henk Barendregt</a></li><li style="font-size:14px;"><b>Per Martin-Löf</b></li><li style="font-size:14px;"><b>Christine Paulin-Mohring</b></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/anders/anders.pdf">Anders Mörtberg</a></li><li style="font-size:14px;"><b>Dan Kan</b></li><li style="font-size:14px;"><b>Jack Morava</b></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/urs/urs.pdf">Urs Schreiber</a></li><li style="font-size:14px;"><b>Fabien Morel</b></li></ol><ol class="type__col"><h3>Mathematics</h3><li style="font-size:14px;"><a href="https://groupoid.space/articles/hom/hom.pdf">Algebra vs Geometry</a></li><li style="font-size:14px;"><b>Set Theory</b></li><li style="font-size:14px;"><b>Topos Theory</b></li><li style="font-size:14px;"><b>Simple Finite Groups</b></li><li style="font-size:14px;"><b>Categories with Families</b></li><li style="font-size:14px;"><b>Heterogeneous Equality</b></li><li style="font-size:14px;"><b>Abelian Groups</b></li><li style="font-size:14px;"><b>Abelian Categories</b></li><li style="font-size:14px;"><b>Supergeometry</b></li><li style="font-size:14px;"><b>C-Systems</b></li><li style="font-size:14px;"><b>Grothendieck Group</b></li></ol></div><br><br></div><div class="exe"><section><h1>BOOKS</h1><p>As a result, a contribution is made to Book Volumes as example
+series of articles on foundation and mathematics of Homotopy Type Theory.</p><br><br></div><div class="types"><div class="type"><ol class="type__col"><h3>Foundations</h3><li style="font-size:14px;"><a href="https://groupoid.space/articles/mltt/mltt.pdf">Type Theory</a></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/cic/cic.pdf">Inductive Types</a></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/hott/hott.pdf">Homotopy Type Theory</a></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/hit/hit.pdf">Higher Inductive Types</a></li><li style="font-size:14px;"><b>Modalities</b></li></ol><ol class="type__col"><h3>Languages</h3><li style="font-size:14px;"><a href="https://groupoid.space/articles/laurent/laurent.pdf">Laurent Schwartz</a></li><li style="font-size:14px;"><b>Ernst Zermelo</b></li><li style="font-size:14px;"><b>Paul Cohen</b></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/henk/henk.pdf">Henk Barendregt</a></li><li style="font-size:14px;"><b>Per Martin-Löf</b></li><li style="font-size:14px;"><b>Christine Paulin-Mohring</b></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/anders/anders.pdf">Anders Mörtberg</a></li><li style="font-size:14px;"><b>Dan Kan</b></li><li style="font-size:14px;"><b>Jack Morava</b></li><li style="font-size:14px;"><a href="https://groupoid.space/articles/urs/urs.pdf">Urs Schreiber</a></li><li style="font-size:14px;"><b>Fabien Morel</b></li></ol><ol class="type__col"><h3>Mathematics</h3><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/spt.pdf">Algebra vs Geometry</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/topos.pdf">Topos Theory</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/cwf.pdf">Categories with Families</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/cwr.pdf">Categories with Reprepresentable Maps</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/id.pdf">Heterogeneous Equality</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/abelian.pdf">Abelian Groups</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/comprehension.pdf">Comprehension Categories</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/cube.pdf">Cosmic Cube</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/fibered.pdf">Fibered Categories</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/jean.pdf">Chevalley Descent</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/lccc.pdf">Local Cartesian Closed Categories</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/smc.pdf">Symmetric Monoidal Categories</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/modal.pdf">Cohesive Topoi</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/quillen.pdf">Quillen Model Structure</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/scheme.pdf">Grothendieck Schemes</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/simplicial.pdf">Simplicial Homotopy Theory</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/stable.pdf">Cohomology and Spectra</a></li><li style="font-size:14px;"><a href="https://groupoid.space/books/vol4/yoga.pdf">Grothendieck Yoga</a></li></ol></div><br><br></div><div class="exe"><section><h1>BOOKS</h1><p>As a result, a contribution is made to Book Volumes as example
 of formalization in AXIO/1 formal system.
 The two common Foundations cores are: 1) MLTT (for set valued mathematics)
 and 2) HoTT (for higher groupoid valued mathematics). Both are given in Volume I.</p><br><div style="padding-top: 8px;"><img src="https://anders.groupoid.space/images/pdf.jpg" width="35"><a href="https://groupoid.space/books/vol1/vol1.pdf">&nbsp; Volume I: Foundations</a></div><br><p>The Volume II coutains articles dedicated to operating

index.html

@@ -341,17 +341,25 @@ block content
                                      'Urs Schreiber': 'https://groupoid.space/articles/urs/urs.pdf',
                                      'Fabien Morel': '' },
 
-                    'Mathematics': { 'Algebra vs Geometry': 'https://groupoid.space/articles/hom/hom.pdf',
-                                     'Set Theory': '',
-                                     'Topos Theory': '',
-                                     'Simple Finite Groups': '',
-                                     'Categories with Families': '',
-                                     'Heterogeneous Equality': '',
-                                     'Abelian Groups': '',
-                                     'Abelian Categories': '',
-                                     'Supergeometry': '',
-                                     'C-Systems': '',
-                                     'Grothendieck Group': '' }
+                    'Mathematics': { 'Algebra vs Geometry': 'https://groupoid.space/books/vol4/spt.pdf',
+                                     'Topos Theory': 'https://groupoid.space/books/vol4/topos.pdf',
+                                     'Categories with Families': 'https://groupoid.space/books/vol4/cwf.pdf',
+                                     'Categories with Reprepresentable Maps': 'https://groupoid.space/books/vol4/cwr.pdf',
+                                     'Heterogeneous Equality': 'https://groupoid.space/books/vol4/id.pdf',
+                                     'Abelian Groups': 'https://groupoid.space/books/vol4/abelian.pdf',
+                                     'Comprehension Categories': 'https://groupoid.space/books/vol4/comprehension.pdf',
+                                     'Cosmic Cube': 'https://groupoid.space/books/vol4/cube.pdf',
+                                     'Fibered Categories': 'https://groupoid.space/books/vol4/fibered.pdf',
+                                     'Chevalley Descent': 'https://groupoid.space/books/vol4/jean.pdf',
+                                     'Local Cartesian Closed Categories': 'https://groupoid.space/books/vol4/lccc.pdf',
+                                     'Symmetric Monoidal Categories': 'https://groupoid.space/books/vol4/smc.pdf',
+                                     'Cohesive Topoi': 'https://groupoid.space/books/vol4/modal.pdf',
+                                     'Quillen Model Structure': 'https://groupoid.space/books/vol4/quillen.pdf',
+                                     'Grothendieck Schemes': 'https://groupoid.space/books/vol4/scheme.pdf',
+                                     'Simplicial Homotopy Theory': 'https://groupoid.space/books/vol4/simplicial.pdf',
+                                     'Cohomology and Spectra': 'https://groupoid.space/books/vol4/stable.pdf',
+                                     'Grothendieck Yoga': 'https://groupoid.space/books/vol4/yoga.pdf',
+                                    }
                                  };