always pass nlab_link and description in category yaml file, null is allowed

ScriptRaccoon · ScriptRaccoon · commit b7258a14bb08 · 2026-05-11T15:26:09.000+02:00
diff --git a/databases/catdat/data/categories/2.yaml b/databases/catdat/data/categories/2.yaml
@@ -4,6 +4,7 @@ notation: $\2$
 objects: two objects $0$ and $1$
 morphisms: only the two identity morphisms
 description: A concrete representation is the full subcategory of $\CRing$ consisting of the two fields $\IF_2$ and $\IF_3$.
+nlab_link: null
 
 tags:
   - finite
diff --git a/databases/catdat/data/categories/Ab_fg.yaml b/databases/catdat/data/categories/Ab_fg.yaml
@@ -3,6 +3,7 @@ name: category of finitely generated abelian groups
 notation: $\Ab_{\fg}$
 objects: finitely generated abelian groups
 morphisms: group homomorphisms
+description: null
 nlab_link: https://ncatlab.org/nlab/show/finitely+generated+module
 
 tags:
diff --git a/databases/catdat/data/categories/BN.yaml b/databases/catdat/data/categories/BN.yaml
@@ -4,6 +4,7 @@ notation: $B\IN$
 objects: a single object
 morphisms: the natural numbers, with addition serving as composition
 description: Every monoid $M$ induces a category $BM$ with a single object $*$, morphisms given by the elements of $M$, and composition given by the monoid operation. Some of the properties of this category depend on the specific monoid. In this example, we take the commutative monoid $M = (\IN,+,0)$, so composition is $n \circ m = n + m$.
+nlab_link: null
 
 tags:
   - category theory
diff --git a/databases/catdat/data/categories/BOn.yaml b/databases/catdat/data/categories/BOn.yaml
@@ -4,6 +4,7 @@ notation: $B\On$
 objects: a single object
 morphisms: ordinal numbers, with addition as composition
 description: Every monoid $M$ induces a category $BM$ with a single object $*$. This also works when $M$ is large, in which case $BM$ is not locally small. In this example, we apply this construction to the large monoid of ordinal numbers with respect to addition, so composition is $\alpha \circ \beta = \alpha + \beta$.
+nlab_link: null
 
 tags:
   - set theory
diff --git a/databases/catdat/data/categories/CMon.yaml b/databases/catdat/data/categories/CMon.yaml
@@ -3,6 +3,7 @@ name: category of commutative monoids
 notation: $\CMon$
 objects: commutative monoids
 morphisms: monoid homomorphisms
+description: null
 nlab_link: https://ncatlab.org/nlab/show/category+of+monoids
 
 tags:
diff --git a/databases/catdat/data/categories/CRing.yaml b/databases/catdat/data/categories/CRing.yaml
@@ -3,6 +3,7 @@ name: category of commutative rings
 notation: $\CRing$
 objects: commutative rings
 morphisms: ring homomorphisms
+description: null
 nlab_link: https://ncatlab.org/nlab/show/CRing
 
 tags:
diff --git a/databases/catdat/data/categories/FI.yaml b/databases/catdat/data/categories/FI.yaml
@@ -4,6 +4,7 @@ notation: $\FI$
 objects: finite sets
 morphisms: injective maps
 description: This category is badly-behaved in itself, but plays an important role in representation theory.
+nlab_link: null
 
 tags:
   - combinatorics
diff --git a/databases/catdat/data/categories/FS.yaml b/databases/catdat/data/categories/FS.yaml
@@ -4,6 +4,7 @@ notation: $\FS$
 objects: finite sets
 morphisms: surjective maps
 description: This category is badly-behaved in itself, but it appears in representation theory. It has two connected components, consisting of the empty set and the non-empty finite sets.
+nlab_link: null
 
 tags:
   - combinatorics
diff --git a/databases/catdat/data/categories/FinAb.yaml b/databases/catdat/data/categories/FinAb.yaml
@@ -3,6 +3,7 @@ name: category of finite abelian groups
 notation: $\FinAb$
 objects: finite abelian groups
 morphisms: group homomorphisms
+description: null
 nlab_link: https://ncatlab.org/nlab/show/finite+abelian+group
 
 tags:
diff --git a/databases/catdat/data/categories/FinGrp.yaml b/databases/catdat/data/categories/FinGrp.yaml
@@ -3,6 +3,7 @@ name: category of finite groups
 notation: $\FinGrp$
 objects: finite groups
 morphisms: group homomorphisms
+description: null
 nlab_link: https://ncatlab.org/nlab/show/finite+group
 
 tags:
diff --git a/databases/catdat/data/categories/FinSet.yaml b/databases/catdat/data/categories/FinSet.yaml
@@ -3,6 +3,7 @@ name: category of finite sets
 notation: $\FinSet$
 objects: finite sets
 morphisms: maps
+description: null
 nlab_link: https://ncatlab.org/nlab/show/FinSet
 
 tags:
diff --git a/databases/catdat/data/categories/FreeAb.yaml b/databases/catdat/data/categories/FreeAb.yaml
@@ -3,6 +3,8 @@ name: category of free abelian groups
 notation: $\FreeAb$
 objects: free abelian groups
 morphisms: group homomorphisms
+description: null
+nlab_link: null
 
 tags:
   - algebra
diff --git a/databases/catdat/data/categories/LRS.yaml b/databases/catdat/data/categories/LRS.yaml
@@ -3,6 +3,7 @@ name: category of locally ringed spaces
 notation: $\LRS$
 objects: locally ringed spaces
 morphisms: morphisms of locally ringed spaces, thus consisting of a continuous map and a homomorphism of sheaves that induces local ring homomorphisms in the stalks
+description: null
 nlab_link: https://ncatlab.org/nlab/show/locally+ringed+topological+space
 
 tags:
diff --git a/databases/catdat/data/categories/Mon.yaml b/databases/catdat/data/categories/Mon.yaml
@@ -3,6 +3,7 @@ name: category of monoids
 notation: $\Mon$
 objects: monoids
 morphisms: monoid homomorphisms
+description: null
 nlab_link: https://ncatlab.org/nlab/show/category+of+monoids
 
 tags:
diff --git a/databases/catdat/data/categories/N.yaml b/databases/catdat/data/categories/N.yaml
@@ -4,6 +4,7 @@ notation: $(\IN,\leq)$
 objects: natural numbers $0, 1, 2, \dotsc$
 morphisms: 'a unique morphism $(n,m) : n \to m$ if $n \leq m$'
 description: This can also be seen as the path category of the infinite linear graph $\bullet \to \bullet \to \bullet \to \cdots$.
+nlab_link: null
 
 tags:
   - number theory
diff --git a/databases/catdat/data/categories/N_oo.yaml b/databases/catdat/data/categories/N_oo.yaml
@@ -3,6 +3,8 @@ name: poset of extended natural numbers
 notation: $(\IN_\infty, \leq)$
 objects: natural numbers and $\infty$
 morphisms: 'a unique morphism $(n, m) : n \to m$ if $n \leq m$, where of course $n \leq \infty$ for all $n$'
+description: null
+nlab_link: null
 
 tags:
   - number theory
diff --git a/databases/catdat/data/categories/On.yaml b/databases/catdat/data/categories/On.yaml
@@ -4,6 +4,7 @@ notation: $(\On,\leq)$
 objects: ordinal numbers
 morphisms: 'a unique morphism $(\alpha,\beta): \alpha \to \beta$ if $\alpha \leq \beta$'
 description: This is a large variant of the poset of natural numbers.
+nlab_link: null
 
 tags:
   - set theory
diff --git a/databases/catdat/data/categories/PMet.yaml b/databases/catdat/data/categories/PMet.yaml
@@ -4,6 +4,7 @@ notation: $\PMet$
 objects: pseudo-metric spaces
 morphisms: non-expansive maps $f$, meaning $d(f(x),f(y)) \leq d(x,y)$ for all $x,y$
 description: In contrast to metric spaces, we do not demand $d(x,y)=0 \implies x=y$ here.
+nlab_link: null
 
 tags:
   - analysis
diff --git a/databases/catdat/data/categories/Rng.yaml b/databases/catdat/data/categories/Rng.yaml
@@ -3,6 +3,7 @@ name: category of rngs
 notation: $\Rng$
 objects: rngs, that is, non-unital rings
 morphisms: maps that preserve addition and multiplication
+description: null
 nlab_link: https://ncatlab.org/nlab/show/Rng
 
 tags:
diff --git a/databases/catdat/data/categories/Sch.yaml b/databases/catdat/data/categories/Sch.yaml
@@ -3,6 +3,7 @@ name: category of schemes
 notation: $\Sch$
 objects: schemes
 morphisms: morphisms of locally ringed spaces
+description: null
 nlab_link: https://ncatlab.org/nlab/show/scheme
 
 tags:
diff --git a/databases/catdat/data/categories/Set_c.yaml b/databases/catdat/data/categories/Set_c.yaml
@@ -4,6 +4,7 @@ notation: $\Set_\c$
 objects: countable sets
 morphisms: maps
 description: A set is countable if it admits a surjection from $\IN$. In particular, every finite set is countable.
+nlab_link: null
 
 tags:
   - set theory
diff --git a/databases/catdat/data/categories/Set_f.yaml b/databases/catdat/data/categories/Set_f.yaml
@@ -4,6 +4,7 @@ notation: $\Set_\f$
 objects: sets
 morphisms: 'maps $f : X \to Y$ with the property that for every $y \in Y$ the fiber $f^*(\{y\})$ is a finite set'
 description: In this variant of $\Set$ we only consider maps with finite fibers, which are commonly called <i>finite-to-one</i>. Equivalently, every preimage of a finite set is again finite, and this description makes it obvious that composition is well-defined.
+nlab_link: null
 
 tags:
   - set theory
diff --git a/databases/catdat/data/categories/SetxSet.yaml b/databases/catdat/data/categories/SetxSet.yaml
@@ -4,6 +4,7 @@ notation: $\Set \times \Set$
 objects: pairs $(A,B)$ of sets $A$ and $B$
 morphisms: A morphism $(A,B) \to (C,D)$ consists of a map $A \to C$ and a map $B \to D$.
 description: This is an example of the <a href="https://ncatlab.org/nlab/show/product+category" target="_blank">product of categories</a>. It inherits most (but not all) properties from $\Set$. It can also be seen as the category $\Sh(1+1)$ of sheaves on a discrete space with two points, and also as the slice category $\Set/(1+1)$.
+nlab_link: null
 
 tags:
   - set theory
diff --git a/databases/catdat/data/categories/Z.yaml b/databases/catdat/data/categories/Z.yaml
@@ -4,6 +4,7 @@ notation: $[\CRing, \Set]$
 objects: Z-functors, i.e. functors from commutative rings to sets
 morphisms: natural transformations
 description: This category is used in functorial algebraic geometry. It also provides a typical example of a functor category that is not locally small, but nevertheless relevant. Most of its properties are directly derived from the category of sets, so other functor categories $[\C, \Set]$ for large categories $\C$ will be similar.
+nlab_link: null
 
 tags:
   - algebraic geometry
diff --git a/databases/catdat/data/categories/Z_div.yaml b/databases/catdat/data/categories/Z_div.yaml
@@ -4,6 +4,7 @@ notation: $(\IZ,\mid)$
 objects: integers
 morphisms: 'a unique morphism $(a,b) : a \to b$ if $a$ divides $b$'
 description: This is a proset, not a poset, because $a$ and $-a$ divide each other, but are not equal for $a \neq 0$. Notice that this category is equivalent (but not isomorphic) to $(\IN,\mid)$.
+nlab_link: null
 
 tags:
   - number theory
diff --git a/databases/catdat/data/categories/sSet.yaml b/databases/catdat/data/categories/sSet.yaml
@@ -3,6 +3,7 @@ name: category of simplicial sets
 notation: $\sSet$
 objects: simplicial sets, i.e. functors $\Delta^{\op} \to \Set$ where $\Delta$ is the <a href="/category/Delta">simplex category</a>
 morphisms: natural transformations
+description: null
 nlab_link: https://ncatlab.org/nlab/show/SimpSet
 
 tags:
diff --git a/databases/catdat/data/categories/walking_coreflexive_pair.yaml b/databases/catdat/data/categories/walking_coreflexive_pair.yaml
@@ -7,7 +7,7 @@ description: >-
   This category is equal to the truncated simplex category $\Delta^{\leq 1}$, i.e. the full subcategory of $\Delta$ spanned by $[0] = \{0\}$ and $[1] = \{0 < 1\}$; this also explains our notation of the category and its objects.
   $$[0] \begin{array}{c} \xhookrightarrow{~~i~~} \\ \xtwoheadleftarrow{~~p~~} \\ \xhookrightarrow{~~j~~} \end{array} [1]$$
   The morphisms $i,j$ are the two inclusions, $p$ is their unique retraction, and $ip,jp : [1] \to [1]$ are the two constant maps. The name of this category comes from the fact that a functor out of it is the same as a <a href="https://ncatlab.org/nlab/show/reflexive+pair" target="_blank">coreflexive pair</a> in the target category. Its dual is therefore the walking reflexive pair.
-
+nlab_link: null
 tags:
   - category theory
   - finite
diff --git a/databases/catdat/data/categories/walking_fork.yaml b/databases/catdat/data/categories/walking_fork.yaml
@@ -4,6 +4,7 @@ notation: $\{0 \to 1 \rightrightarrows 2\}$
 objects: three objects $0,1,2$
 morphisms: 'one morphism $i : 0 \to 1$, two morphisms $f,g : 1 \rightrightarrows 2$, one morphism $0 \to 2$ (namely, $f \circ i = g \circ i$), and the identities'
 description: The name of this category comes from the fact that a functor out of it is the same as a <a href="https://ncatlab.org/nlab/show/fork" target="_blank">fork</a>.
+nlab_link: null
 
 tags:
   - category theory
diff --git a/databases/catdat/data/categories/walking_idempotent.yaml b/databases/catdat/data/categories/walking_idempotent.yaml
@@ -4,6 +4,7 @@ notation: $\Idem$
 objects: a single object $0$
 morphisms: 'two morphisms $\id_0,e : 0 \to 0$ with $e^2=e$'
 description: The name of this category comes from the fact that a functor out of it is the same as an <a href="https://ncatlab.org/nlab/show/idempotent" target="_blank">idempotent morphism</a> in the target category. It can also be seen as the delooping of the monoid $\{1,e\}$ in which $e^2=e$.
+nlab_link: null
 
 tags:
   - category theory
diff --git a/databases/catdat/data/categories/walking_splitting.yaml b/databases/catdat/data/categories/walking_splitting.yaml
@@ -6,7 +6,7 @@ morphisms: 'the identities, morphisms $i : 0 \to 1$, $p : 1 \to 0$ satisfying $p
 description: |-
   This category could also be called the "walking split idempotent" (or "walking section", "walking retraction"), but we chose a name that emphasizes that the splitting belongs to the data. Notice that the $5$ given morphisms are indeed closed under composition. For example, $p \circ ip = p$ and $ip \circ i = i$.
   The walking splitting can be interpreted as a skeleton of the category of $\IF_2$-vector spaces of dimension $\leq 1$.
-
+nlab_link: null
 tags:
   - category theory
   - finite
diff --git a/databases/catdat/scripts/seed.ts b/databases/catdat/scripts/seed.ts
@@ -204,8 +204,8 @@ function seed_categories() {
 			category.notation,
 			category.objects,
 			category.morphisms,
-			category.description || null,
-			category.nlab_link || null,
+			category.description,
+			category.nlab_link,
 			category.dual_category_id || null,
 		)
 
diff --git a/databases/catdat/scripts/seed.types.ts b/databases/catdat/scripts/seed.types.ts
@@ -21,8 +21,8 @@ export type CategoryYaml = {
 	notation: string
 	objects: string
 	morphisms: string
-	description?: string | null
-	nlab_link?: string
+	description: string | null
+	nlab_link: string | null
 	dual_category_id?: string | null
 	tags: string[]
 	related_categories: string[]
