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Add many row templates.

Binary files a/catabase.db and b/catabase.db differ

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+++ b/templates/row-catabase-categories_of_groups.html

		@@ -0,0 +1,18 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set cat = display_rows[0]["parent"] %}
	6	+{% set grpcat = display_rows[0]["internal_groups"] %}
	7	+
	8	+<h1>Category of Groups: {{ grpcat }}</h1>
	9	+
	10	+<p>{{ grpcat }} is a subcategory of {{ cat }} whose objects are all internal
	11	+groups:</p>
	12	+
	13	+<div class="bigmath">
	14	+ Grp({{ cat }}) ≅ {{ grpcat }}
	15	+</div>
	16	+
	17	+{{ super() }}
	18	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-categories_of_monoids.html

		@@ -0,0 +1,21 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set cat = display_rows[0]["parent"] %}
	6	+{% set moncat = display_rows[0]["internal_monoids"] %}
	7	+
	8	+<h1>Category of Monoids: {{ moncat }}</h1>
	9	+
	10	+<p>{{ moncat }} is a subcategory of {{ cat }} whose objects are all internal
	11	+monoids:</p>
	12	+
	13	+<div class="bigmath">
	14	+ Mon({{ cat }}) ≅ {{ moncat }}
	15	+</div>
	16	+
	17	+<p>Note that {{ cat }} must be a monoidal category in order to even have
	18	+internal monoids. This is an instance of the Microcosm Principle.</p>
	19	+
	20	+{{ super() }}
	21	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-categories_of_simplicial_objects.html

		@@ -0,0 +1,20 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set cat = display_rows[0]["parent"] %}
	6	+{% set sscat = display_rows[0]["internal_simplicial_sets"] %}
	7	+
	8	+<h1>Category of Simplicial Objects: {{ sscat }}</h1>
	9	+
	10	+<p>{{ sscat }} is a full subcategory of {{ cat }} whose objects are all
	11	+internal simplicial objects. A simplicial object in {{ cat }} is a
	12	+contravariant functor from Δ to {{ cat }}, so the category of simplicial
	13	+objects is a contravariant functor category:</p>
	14	+
	15	+<div class="bigmath">
	16	+ {{ sscat }} ≅ [Δ°, {{ cat }}]
	17	+</div>
	18	+
	19	+{{ super() }}
	20	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-equivalent_categories.html

		@@ -0,0 +1,17 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set cat1 = display_rows[0]["cat1"] %}
	6	+{% set cat2 = display_rows[0]["cat2"] %}
	7	+
	8	+<h1>Equivalence of Categories: {{ cat1 }} ≅ {{ cat2 }}</h1>
	9	+
	10	+<p>{{ cat1 }} is equivalent to {{ cat2 }}, and vice versa.</p>
	11	+
	12	+<div class="bigmath">
	13	+ {{ cat1 }} ≅ {{ cat2 }}
	14	+</div>
	15	+
	16	+{{ super() }}
	17	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-full_subcategories.html

		@@ -0,0 +1,16 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set sub = display_rows[0]["subcategory"] %}
	6	+{% set sup = display_rows[0]["supercategory"] %}
	7	+
	8	+<h1>Full Subcategory: {{ sub }} ⊊ {{ sup }}</h1>
	9	+
	10	+<p>{{ sub }} is a full subcategory of {{ sup }}. When any two objects of
	11	+{{ sup }} are in {{ sub }}, so is every arrow between them. Put another way,
	12	+{{ sub }} has only some of the objects of {{ sup }}, but all of the
	13	+arrows.</p>
	14	+
	15	+{{ super() }}
	16	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-limits.html

		@@ -0,0 +1,18 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set diagram = display_rows[0]["diagram"] %}
	6	+{% set is_colimit = display_rows[0]["is_colimit"] %}
	7	+{% set construction = display_rows[0]["construction"] %}
	8	+{% set lim = "colimit" if is_colimit else "limit" %}
	9	+{% set Lim = "Colimit" if is_colimit else "Limit" %}
	10	+
	11	+<h1>{{ Lim }}: {{ construction }}</h1>
	12	+
	13	+<p>A {{ construction }} is a kind of {{ lim }}. Given a {{ diagram }},
	14	+considered as a diagram in some category, a {{ construction }} is the
	15	+{{ lim }} of that {{ diagram }} in that category.</p>
	16	+
	17	+{{ super() }}
	18	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-opposite_categories.html

		@@ -0,0 +1,21 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set cat = display_rows[0]["category"] %}
	6	+{% set opcat = display_rows[0]["op"] %}
	7	+
	8	+{% if cat == opcat %}
	9	+<h1>Self-Opposite Category: {{ cat }}</h1>
	10	+
	11	+<p>{{ cat }} is equivalent to its opposite category.</p>
	12	+{% else %}
	13	+<h1>Opposite Categories: {{ cat }} & {{ opcat }}</h1>
	14	+
	15	+<p>{{ cat }} and {{ opcat }} are opposites; they are equivalent, except that
	16	+the arrows in {{ cat }} are pointed in the opposite direction from in
	17	+{{ opcat }}.</p>
	18	+{% endif %}
	19	+
	20	+{{ super() }}
	21	+{% endblock %}

--- /dev/null

+++ b/templates/row-catabase-skeletons.html

		@@ -0,0 +1,20 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set skel = display_rows[0]["skeleton"] %}
	6	+{% set cat = display_rows[0]["category"] %}
	7	+
	8	+<h1>Skeleton: {{ skel }}</h1>
	9	+
	10	+<p>{{ skel }} is a skeleton of {{ cat }}; {{ skel }} is equivalent to
	11	+{{ cat }} but has no isomorphisms. Less cryptically, isomorphic objects in
	12	+{{ cat }} are mapped to single objects in {{ skel }} representing their
	13	+equivalence classes.</p>
	14	+
	15	+<p>Skeletons are not quite functorial, because their construction requires the
	16	+Axiom of Choice.</p>
	17	+
	18	+{{ super() }}
	19	+{% endblock %}
	20	+

--- /dev/null

+++ b/templates/row-catabase-topoi.html

		@@ -0,0 +1,28 @@
	1	+{% extends "default:row.html" %}
	2	+
	3	+{% block content %}
	4	+
	5	+{% set topos = display_rows[0]["category"] %}
	6	+<h1>Topos: {{ topos }}</h1>
	7	+
	8	+<p>{{ topos }} is a topos.</p>
	9	+
	10	+{% if display_rows[0]["is_grothendieck"] %}
	11	+<p>{{ topos }} is Grothendieck; it acts like a category of sheaves.</p>
	12	+{% endif %}
	13	+
	14	+{% if display_rows[0]["has_nno"] %}
	15	+<p>{{ topos }} has a natural numbers object.</p>
	16	+{% endif %}
	17	+
	18	+{% if display_rows[0]["is_boolean"] %}
	19	+<p>{{ topos }} is Boolean; the Law of Excluded Middle is valid within
	20	+{{ topos }}.</p>
	21	+{% endif %}
	22	+
	23	+{% if display_rows[0]["is_well_pointed"] %}
	24	+<p>{{ topos }} is well-pointed.</p>
	25	+{% endif %}
	26	+
	27	+{{ super() }}
	28	+{% endblock %}