diff --git a/docs/about/limits.md b/docs/about/limits.md
index 39f7f6f1..90e02435 100644
--- a/docs/about/limits.md
+++ b/docs/about/limits.md
@@ -32,8 +32,8 @@ costs to add.
   `variables:` or `given_variables:`. One enters where it says something no
   section already says, where a file decides it without data, and where the
   typesetter prints it. `given_variables:` entered on all three: nothing else
-  states that a column belongs to another file, which is what lets a template
-  load and print on its own.
+  states that a column belongs to another file, which is what lets a component
+  file load and print on its own.
 
 A request that is none of the three is refused, and the
 [table of refusals](#deliberate-non-primitives) records it with what to write
@@ -174,10 +174,10 @@ That another tool has a feature is not by itself a reason to add it.
 
 ## Composition (component libraries)
 
-A component library is a set of templates, such as a boiler, a battery and a
-line, that agree on how ports and flows are named. You merge the templates you
-need into one file, wire the components together with a connectivity table in
-the data, and close the system with one `sum(by=)` balance.
+A component library is a set of files, one per component type — a boiler, a
+battery, a line — that agree on how ports and flows are named. You merge the
+files you need into one, wire the components together with a connectivity table
+in the data, and close the system with one `sum(by=)` balance.
 
 The topology is data. Adding a second battery is a row in a table, not a second
 block of YAML, so the file grows with the number of component _types_ and not
@@ -189,16 +189,16 @@ a path, so a model assembled in Python is checked exactly as a file is, and
 file may hold. There is no Python API that builds models any other way.
 
 Two verbs do this, and they answer different questions. `merge` composes
-peers, so a name two templates declare is a collision and the order they are
+peers, so a name two fragments declare is a collision and the order they are
 given in means nothing. `override` lays patches over a base, which is what a
 framework ships and a project extends, a field at a time.
 [Compose a model from several files](../howto/compose.md) is the recipe for
 both.
 
-A template reads the coupling surface it is written against, and declares that
-column under `given_variables:`. So a template loads on its own, and prints as
-math on its own, which is what it could not do while a fragment was a file the
-loader had to refuse. `merge` folds each given declaration into the one that
+A component file reads the coupling surface it is written against, and declares
+that column under `given_variables:`. So it loads on its own, and prints as math
+on its own, which is what it could not do while a fragment was a file the loader
+had to refuse. `merge` folds each given declaration into the one that
 introduces it, so a composed library carries none.
 
 A layer over a model this language never sees — one built through linopy, say —
@@ -219,8 +219,8 @@ exactly, never changed, because the expressions written over an axis are
 already in the base.
 
 Two requests were closed against this design. A built-in merge (#30) and
-namespaces so that two templates can each declare a `p` (#29) are both things a
+namespaces so that two fragments can each declare a `p` (#29) are both things a
 library does before it hands over a `dict`. Arithmetic in `bounds:`, which signed
 and bidirectional flows need, is still open as #31. A component whose number of
 ports is only known at run time belongs in the library, which emits more rows or
-more templates, and never one block of YAML per component.
+more files, and never one block of YAML per component.
diff --git a/docs/examples/index.md b/docs/examples/index.md
index d6c5e3a9..178bcfde 100644
--- a/docs/examples/index.md
+++ b/docs/examples/index.md
@@ -23,8 +23,8 @@ or starts printing different math fails CI.
   declaration at a time. PyPSA's name for each row sits beside the YAML and the
   equation.
 - [A component library](library/index.md) is several files that compose into
-  one model. Each template reads the coupling surface and prints on its own,
-  and the composed page shows what `merge` returns.
+  one model. Each file reads the coupling surface and prints on its own, and the
+  composed page shows what `merge` returns.
 
 The math on these pages is printed by the typesetter from the file above it. See
 [Typeset the math](../reference/typeset.md) to print your own.
diff --git a/docs/howto/compose.md b/docs/howto/compose.md
index 3eb83eb9..ad80df4b 100644
--- a/docs/howto/compose.md
+++ b/docs/howto/compose.md
@@ -6,13 +6,13 @@ SPDX-License-Identifier: CC-BY-4.0
 # Compose a model from several files
 
 Build one model out of files that each say part of it. `merge` composes
-**peers** — the templates of a component library, where a name two of them
-declare is a collision. `override` lays **patches** over a base — what a
+**peers** — the files of a component library, where a name two of them declare
+is a collision. `override` lays **patches** over a base — what a
 framework ships and a project extends. Both hand back one mapping, which
 [`to_spec`](../reference/language/reading.md) loads like any file, and they
 compose: `override(merge({…}), {…})`.
 
-## A library of templates
+## A library of components
 
 1. **Write the coupling surface as a model.** One flow per port, one balance
    per bus. Nothing in it knows which components exist.
@@ -131,12 +131,12 @@ compose: `override(merge({…}), {…})`.
 Fragments own their math, so a name two of them declare is refused, both named. Here two files each say what a generator fleet is:
 
 ```text
-fragments 'gas' and 'coal' both declare the parameter 'Generator_p_nom'. Two of the same kind of thing are two rows of a dimension rather than two fragments: merge the template once, and let the data carry both. Different math under one spelling is a rename — call one of them something else.
+fragments 'gas' and 'coal' both declare the parameter 'Generator_p_nom'. Two of the same kind of thing are two rows of a dimension rather than two fragments: merge the fragment once, and let the data carry both. Different math under one spelling is a rename — call one of them something else.
 ```
 
 ## A column read one way and introduced another
 
-What a template states about a column it reads has to agree with the file that
+What a fragment states about a column it reads has to agree with the file that
 owns it:
 
 ```text
diff --git a/docs/reference/language/declarations.md b/docs/reference/language/declarations.md
index 9d87d250..65da623a 100644
--- a/docs/reference/language/declarations.md
+++ b/docs/reference/language/declarations.md
@@ -117,7 +117,7 @@ stand in another variable's `bounds`.
 ## `given_variables`
 
 A given variable is a column this file reads and another file introduces. It is
-what lets a template stand on its own: the file loads, and it prints as math,
+what lets a fragment stand on its own: the file loads, and it prints as math,
 without the file that owns the column.
 
 ```yaml
diff --git a/src/math_spec/advice.py b/src/math_spec/advice.py
index 7f119e68..400aec54 100644
--- a/src/math_spec/advice.py
+++ b/src/math_spec/advice.py
@@ -45,7 +45,7 @@ def _given(program: Program) -> list[Advice]:
     """One note per declaration the program reads and does not build.
 
     A note rather than a refusal, because both readings are a model somebody
-    meant: a template is composed with the file that introduces the column, and
+    meant: a fragment is composed with the file that introduces the column, and
     a layer is bound to the model it is laid onto. What neither is, is a model
     a consumer can build alone, and the consumer is the one that can tell which
     it is holding.
@@ -55,7 +55,7 @@ def _given(program: Program) -> list[Advice]:
             'given',
             name,
             f"{kind} '{name}' is read here and built elsewhere: a consumer binds it to the model this "
-            f'one is layered onto, and refuses where it cannot. A template is composed instead, and '
+            f'one is layered onto, and refuses where it cannot. A fragment is composed instead, and '
             f'merge() folds it into the file that introduces it.',
         )
         for kind, group in (('variable', program.given_variables), ('row family', program.given_constraints))
diff --git a/src/math_spec/composition.py b/src/math_spec/composition.py
index d428c427..3268fef8 100644
--- a/src/math_spec/composition.py
+++ b/src/math_spec/composition.py
@@ -5,7 +5,7 @@
 """Several files into one model, before any of them is validated.
 
 Two verbs, and they answer different questions. :func:`merge` composes
-**peers**: templates that each own part of the math, where a name two of them
+**peers**: fragments that each own part of the math, where a name two of them
 declare is a collision and the order they are given in means nothing.
 :func:`override` layers a **base and its patches**: what a framework ships and a
 project extends, where a name the patch declares is the point. Neither is a
@@ -95,14 +95,14 @@ def merge(
 ) -> dict[str, Any]:
     """*fragments* composed as peers, each owning the math it declares.
 
-    A component library is a set of templates that agree on a coupling
-    surface — one flow per port, one balance per bus — and wiring a system is
-    rows in a table rather than generated YAML. This is what takes the
-    templates and hands back one model.
+    A component library is a set of files that agree on a coupling surface —
+    one flow per port, one balance per bus — and wiring a system is rows in a
+    table rather than generated YAML. This is what takes those files and hands
+    back one model.
 
     Args:
         fragments: What each fragment is called, to the fragment. The name is
-            what an error calls it, so it is the template's name rather than a
+            what an error calls it, so it is the fragment's name rather than a
             path. The order they are given in does not reach the result.
         description: What the *composed* model is. A fragment's own
             ``description`` is about the fragment, so it is neither carried nor
@@ -142,7 +142,7 @@ def _one_version(read: Mapping[str, dict[str, Any]]) -> int:
     """The language version every fragment is written against.
 
     A fragment saying nothing is version 0 like any file, so a library pinning
-    one and a template pinning none is the disagreement it looks like rather
+    one and a fragment pinning none is the disagreement it looks like rather
     than a default quietly winning.
     """
     declared = {name: sections.get('version', 0) for name, sections in read.items()}
@@ -198,7 +198,7 @@ def _claimed(read: Mapping[str, dict[str, Any]], section: str) -> dict[str, Any]
                 raise LanguageError(
                     f"fragments '{author[key]}' and '{name}' both declare the {_singular(section)} "
                     f'{key!r}. Two of the same kind of thing are two rows of a dimension rather than '
-                    f'two fragments: merge the template once, and let the data carry both. Different '
+                    f'two fragments: merge the fragment once, and let the data carry both. Different '
                     f'math under one spelling is a rename — call one of them something else.'
                 )
             merged[key] = block
@@ -239,7 +239,7 @@ def _author_of(read: Mapping[str, dict[str, Any]], section: str, key: str) -> st
 def _summed_objective(read: Mapping[str, dict[str, Any]]) -> dict[str, Any] | None:
     """Every fragment's objective, summed, or ``None`` where none declares one.
 
-    Summing is what composing costs: each template prices what it owns, and the
+    Summing is what composing costs: each fragment prices what it owns, and the
     system pays for all of it. The senses must agree, because a sum of two
     objectives has one sense and nothing in the files says which — negating the
     minority would be this function deciding what a model means.
diff --git a/tests/test_given.py b/tests/test_given.py
index 7a30f910..addb3b5f 100644
--- a/tests/test_given.py
+++ b/tests/test_given.py
@@ -4,7 +4,7 @@
 
 """What a file reads and does not build: a column, and a row family.
 
-Two readings, and each is a model somebody meant. A **template** reads a column
+Two readings, and each is a model somebody meant. A **fragment** reads a column
 the file beside it introduces, and `merge` folds the two together, so the
 composed model carries neither the declaration nor any trace of it. A **layer**
 reads a column, or the dual of a row family, that a model outside the language
@@ -21,7 +21,7 @@
 
 from math_spec import FORMATS, LanguageError, advice, merge, to_markdown, to_program, to_spec, typeset
 
-#: One component template: it pins the flow at its own port, and the column it
+#: One component file: it pins the flow at its own port, and the column it
 #: pins belongs to the surface fragment below.
 SUPPLY = {
     'description': 'A fleet of generators, each on one port.',
diff --git a/tests/test_library_example.py b/tests/test_library_example.py
index 8a6738f2..464d68b2 100644
--- a/tests/test_library_example.py
+++ b/tests/test_library_example.py
@@ -32,7 +32,7 @@ def test_every_fragment_loads_and_prints_on_its_own(name):
 
 
 @pytest.mark.parametrize('name', ['generator', 'load'])
-def test_a_component_template_reads_the_surface_and_introduces_no_flow(name):
+def test_a_component_file_reads_the_surface_and_introduces_no_flow(name):
     spec = to_spec(FRAGMENTS[name])
     assert sorted(spec.given_variables) == ['Port_p']
     assert 'Port_p' not in spec.variables, 'the surface introduces the column, and a component file only writes into it'
@@ -48,7 +48,7 @@ def test_the_library_composes_into_one_model():
     )
 
 
-def test_the_balance_is_written_once_however_many_templates_are_merged():
+def test_the_balance_is_written_once_however_many_fragments_are_merged():
     one = to_spec(merge({'surface': FRAGMENTS['surface'], 'load': FRAGMENTS['load']}))
     both = to_spec(merge(FRAGMENTS))
     assert one.constraints['Bus_nodal_balance'].expression == both.constraints['Bus_nodal_balance'].expression