@@ -39,23 +39,23 @@ module _
3939 isLeftSemimoduleHomomorphism f-homo g-homo = record
4040 { +ᴹ-isMonoidHomomorphism = isMonoidHomomorphism ≈ᴹ₃-trans F.+ᴹ-isMonoidHomomorphism G.+ᴹ-isMonoidHomomorphism
4141 ; *ₗ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ₗ-homo r x)) (G.*ₗ-homo r (f x))
42- } where module F = IsLeftSemimoduleHomomorphism f-homo; module G = IsLeftSemimoduleHomomorphism g-homo
42+ } where module F = IsLeftSemimoduleHomomorphism M₁ M₂ f-homo; module G = IsLeftSemimoduleHomomorphism M₂ M₃ g-homo
4343
4444 isLeftSemimoduleMonomorphism : IsLeftSemimoduleMonomorphism M₁ M₂ f →
4545 IsLeftSemimoduleMonomorphism M₂ M₃ g →
4646 IsLeftSemimoduleMonomorphism M₁ M₃ (g ∘ f)
4747 isLeftSemimoduleMonomorphism f-mono g-mono = record
4848 { isLeftSemimoduleHomomorphism = isLeftSemimoduleHomomorphism F.isLeftSemimoduleHomomorphism G.isLeftSemimoduleHomomorphism
4949 ; injective = F.injective ∘ G.injective
50- } where module F = IsLeftSemimoduleMonomorphism f-mono; module G = IsLeftSemimoduleMonomorphism g-mono
50+ } where module F = IsLeftSemimoduleMonomorphism M₁ M₂ f-mono; module G = IsLeftSemimoduleMonomorphism M₂ M₃ g-mono
5151
5252 isLeftSemimoduleIsomorphism : IsLeftSemimoduleIsomorphism M₁ M₂ f →
5353 IsLeftSemimoduleIsomorphism M₂ M₃ g →
5454 IsLeftSemimoduleIsomorphism M₁ M₃ (g ∘ f)
5555 isLeftSemimoduleIsomorphism f-iso g-iso = record
5656 { isLeftSemimoduleMonomorphism = isLeftSemimoduleMonomorphism F.isLeftSemimoduleMonomorphism G.isLeftSemimoduleMonomorphism
5757 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
58- } where module F = IsLeftSemimoduleIsomorphism f-iso; module G = IsLeftSemimoduleIsomorphism g-iso
58+ } where module F = IsLeftSemimoduleIsomorphism M₁ M₂ f-iso; module G = IsLeftSemimoduleIsomorphism M₂ M₃ g-iso
5959
6060module _
6161 {R : Set r}
@@ -74,23 +74,23 @@ module _
7474 isLeftModuleHomomorphism f-homo g-homo = record
7575 { +ᴹ-isGroupHomomorphism = isGroupHomomorphism ≈ᴹ₃-trans F.+ᴹ-isGroupHomomorphism G.+ᴹ-isGroupHomomorphism
7676 ; *ₗ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ₗ-homo r x)) (G.*ₗ-homo r (f x))
77- } where module F = IsLeftModuleHomomorphism f-homo; module G = IsLeftModuleHomomorphism g-homo
77+ } where module F = IsLeftModuleHomomorphism M₁ M₂ f-homo; module G = IsLeftModuleHomomorphism M₂ M₃ g-homo
7878
7979 isLeftModuleMonomorphism : IsLeftModuleMonomorphism M₁ M₂ f →
8080 IsLeftModuleMonomorphism M₂ M₃ g →
8181 IsLeftModuleMonomorphism M₁ M₃ (g ∘ f)
8282 isLeftModuleMonomorphism f-mono g-mono = record
8383 { isLeftModuleHomomorphism = isLeftModuleHomomorphism F.isLeftModuleHomomorphism G.isLeftModuleHomomorphism
8484 ; injective = F.injective ∘ G.injective
85- } where module F = IsLeftModuleMonomorphism f-mono; module G = IsLeftModuleMonomorphism g-mono
85+ } where module F = IsLeftModuleMonomorphism M₁ M₂ f-mono; module G = IsLeftModuleMonomorphism M₂ M₃ g-mono
8686
8787 isLeftModuleIsomorphism : IsLeftModuleIsomorphism M₁ M₂ f →
8888 IsLeftModuleIsomorphism M₂ M₃ g →
8989 IsLeftModuleIsomorphism M₁ M₃ (g ∘ f)
9090 isLeftModuleIsomorphism f-iso g-iso = record
9191 { isLeftModuleMonomorphism = isLeftModuleMonomorphism F.isLeftModuleMonomorphism G.isLeftModuleMonomorphism
9292 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
93- } where module F = IsLeftModuleIsomorphism f-iso; module G = IsLeftModuleIsomorphism g-iso
93+ } where module F = IsLeftModuleIsomorphism M₁ M₂ f-iso; module G = IsLeftModuleIsomorphism M₂ M₃ g-iso
9494
9595module _
9696 {R : Set r}
@@ -109,23 +109,23 @@ module _
109109 isRightSemimoduleHomomorphism f-homo g-homo = record
110110 { +ᴹ-isMonoidHomomorphism = isMonoidHomomorphism ≈ᴹ₃-trans F.+ᴹ-isMonoidHomomorphism G.+ᴹ-isMonoidHomomorphism
111111 ; *ᵣ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ᵣ-homo r x)) (G.*ᵣ-homo r (f x))
112- } where module F = IsRightSemimoduleHomomorphism f-homo; module G = IsRightSemimoduleHomomorphism g-homo
112+ } where module F = IsRightSemimoduleHomomorphism M₁ M₂ f-homo; module G = IsRightSemimoduleHomomorphism M₂ M₃ g-homo
113113
114114 isRightSemimoduleMonomorphism : IsRightSemimoduleMonomorphism M₁ M₂ f →
115115 IsRightSemimoduleMonomorphism M₂ M₃ g →
116116 IsRightSemimoduleMonomorphism M₁ M₃ (g ∘ f)
117117 isRightSemimoduleMonomorphism f-mono g-mono = record
118118 { isRightSemimoduleHomomorphism = isRightSemimoduleHomomorphism F.isRightSemimoduleHomomorphism G.isRightSemimoduleHomomorphism
119119 ; injective = F.injective ∘ G.injective
120- } where module F = IsRightSemimoduleMonomorphism f-mono; module G = IsRightSemimoduleMonomorphism g-mono
120+ } where module F = IsRightSemimoduleMonomorphism M₁ M₂ f-mono; module G = IsRightSemimoduleMonomorphism M₂ M₃ g-mono
121121
122122 isRightSemimoduleIsomorphism : IsRightSemimoduleIsomorphism M₁ M₂ f →
123123 IsRightSemimoduleIsomorphism M₂ M₃ g →
124124 IsRightSemimoduleIsomorphism M₁ M₃ (g ∘ f)
125125 isRightSemimoduleIsomorphism f-iso g-iso = record
126126 { isRightSemimoduleMonomorphism = isRightSemimoduleMonomorphism F.isRightSemimoduleMonomorphism G.isRightSemimoduleMonomorphism
127127 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
128- } where module F = IsRightSemimoduleIsomorphism f-iso; module G = IsRightSemimoduleIsomorphism g-iso
128+ } where module F = IsRightSemimoduleIsomorphism M₁ M₂ f-iso; module G = IsRightSemimoduleIsomorphism M₂ M₃ g-iso
129129
130130module _
131131 {R : Set r}
@@ -144,23 +144,23 @@ module _
144144 isRightModuleHomomorphism f-homo g-homo = record
145145 { +ᴹ-isGroupHomomorphism = isGroupHomomorphism ≈ᴹ₃-trans F.+ᴹ-isGroupHomomorphism G.+ᴹ-isGroupHomomorphism
146146 ; *ᵣ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ᵣ-homo r x)) (G.*ᵣ-homo r (f x))
147- } where module F = IsRightModuleHomomorphism f-homo; module G = IsRightModuleHomomorphism g-homo
147+ } where module F = IsRightModuleHomomorphism M₁ M₂ f-homo; module G = IsRightModuleHomomorphism M₂ M₃ g-homo
148148
149149 isRightModuleMonomorphism : IsRightModuleMonomorphism M₁ M₂ f →
150150 IsRightModuleMonomorphism M₂ M₃ g →
151151 IsRightModuleMonomorphism M₁ M₃ (g ∘ f)
152152 isRightModuleMonomorphism f-mono g-mono = record
153153 { isRightModuleHomomorphism = isRightModuleHomomorphism F.isRightModuleHomomorphism G.isRightModuleHomomorphism
154154 ; injective = F.injective ∘ G.injective
155- } where module F = IsRightModuleMonomorphism f-mono; module G = IsRightModuleMonomorphism g-mono
155+ } where module F = IsRightModuleMonomorphism M₁ M₂ f-mono; module G = IsRightModuleMonomorphism M₂ M₃ g-mono
156156
157157 isRightModuleIsomorphism : IsRightModuleIsomorphism M₁ M₂ f →
158158 IsRightModuleIsomorphism M₂ M₃ g →
159159 IsRightModuleIsomorphism M₁ M₃ (g ∘ f)
160160 isRightModuleIsomorphism f-iso g-iso = record
161161 { isRightModuleMonomorphism = isRightModuleMonomorphism F.isRightModuleMonomorphism G.isRightModuleMonomorphism
162162 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
163- } where module F = IsRightModuleIsomorphism f-iso; module G = IsRightModuleIsomorphism g-iso
163+ } where module F = IsRightModuleIsomorphism M₁ M₂ f-iso; module G = IsRightModuleIsomorphism M₂ M₃ g-iso
164164
165165module _
166166 {R : Set r}
@@ -181,23 +181,23 @@ module _
181181 { +ᴹ-isMonoidHomomorphism = isMonoidHomomorphism ≈ᴹ₃-trans F.+ᴹ-isMonoidHomomorphism G.+ᴹ-isMonoidHomomorphism
182182 ; *ₗ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ₗ-homo r x)) (G.*ₗ-homo r (f x))
183183 ; *ᵣ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ᵣ-homo r x)) (G.*ᵣ-homo r (f x))
184- } where module F = IsBisemimoduleHomomorphism f-homo; module G = IsBisemimoduleHomomorphism g-homo
184+ } where module F = IsBisemimoduleHomomorphism M₁ M₂ f-homo; module G = IsBisemimoduleHomomorphism M₂ M₃ g-homo
185185
186186 isBisemimoduleMonomorphism : IsBisemimoduleMonomorphism M₁ M₂ f →
187187 IsBisemimoduleMonomorphism M₂ M₃ g →
188188 IsBisemimoduleMonomorphism M₁ M₃ (g ∘ f)
189189 isBisemimoduleMonomorphism f-mono g-mono = record
190190 { isBisemimoduleHomomorphism = isBisemimoduleHomomorphism F.isBisemimoduleHomomorphism G.isBisemimoduleHomomorphism
191191 ; injective = F.injective ∘ G.injective
192- } where module F = IsBisemimoduleMonomorphism f-mono; module G = IsBisemimoduleMonomorphism g-mono
192+ } where module F = IsBisemimoduleMonomorphism M₁ M₂ f-mono; module G = IsBisemimoduleMonomorphism M₂ M₃ g-mono
193193
194194 isBisemimoduleIsomorphism : IsBisemimoduleIsomorphism M₁ M₂ f →
195195 IsBisemimoduleIsomorphism M₂ M₃ g →
196196 IsBisemimoduleIsomorphism M₁ M₃ (g ∘ f)
197197 isBisemimoduleIsomorphism f-iso g-iso = record
198198 { isBisemimoduleMonomorphism = isBisemimoduleMonomorphism F.isBisemimoduleMonomorphism G.isBisemimoduleMonomorphism
199199 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
200- } where module F = IsBisemimoduleIsomorphism f-iso; module G = IsBisemimoduleIsomorphism g-iso
200+ } where module F = IsBisemimoduleIsomorphism M₁ M₂ f-iso; module G = IsBisemimoduleIsomorphism M₂ M₃ g-iso
201201
202202module _
203203 {R : Set r}
@@ -218,23 +218,23 @@ module _
218218 { +ᴹ-isGroupHomomorphism = isGroupHomomorphism ≈ᴹ₃-trans F.+ᴹ-isGroupHomomorphism G.+ᴹ-isGroupHomomorphism
219219 ; *ₗ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ₗ-homo r x)) (G.*ₗ-homo r (f x))
220220 ; *ᵣ-homo = λ r x → ≈ᴹ₃-trans (G.⟦⟧-cong (F.*ᵣ-homo r x)) (G.*ᵣ-homo r (f x))
221- } where module F = IsBimoduleHomomorphism f-homo; module G = IsBimoduleHomomorphism g-homo
221+ } where module F = IsBimoduleHomomorphism M₁ M₂ f-homo; module G = IsBimoduleHomomorphism M₂ M₃ g-homo
222222
223223 isBimoduleMonomorphism : IsBimoduleMonomorphism M₁ M₂ f →
224224 IsBimoduleMonomorphism M₂ M₃ g →
225225 IsBimoduleMonomorphism M₁ M₃ (g ∘ f)
226226 isBimoduleMonomorphism f-mono g-mono = record
227227 { isBimoduleHomomorphism = isBimoduleHomomorphism F.isBimoduleHomomorphism G.isBimoduleHomomorphism
228228 ; injective = F.injective ∘ G.injective
229- } where module F = IsBimoduleMonomorphism f-mono; module G = IsBimoduleMonomorphism g-mono
229+ } where module F = IsBimoduleMonomorphism M₁ M₂ f-mono; module G = IsBimoduleMonomorphism M₂ M₃ g-mono
230230
231231 isBimoduleIsomorphism : IsBimoduleIsomorphism M₁ M₂ f →
232232 IsBimoduleIsomorphism M₂ M₃ g →
233233 IsBimoduleIsomorphism M₁ M₃ (g ∘ f)
234234 isBimoduleIsomorphism f-iso g-iso = record
235235 { isBimoduleMonomorphism = isBimoduleMonomorphism F.isBimoduleMonomorphism G.isBimoduleMonomorphism
236236 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
237- } where module F = IsBimoduleIsomorphism f-iso; module G = IsBimoduleIsomorphism g-iso
237+ } where module F = IsBimoduleIsomorphism M₁ M₂ f-iso; module G = IsBimoduleIsomorphism M₂ M₃ g-iso
238238
239239module _
240240 {R : Set r}
@@ -252,23 +252,23 @@ module _
252252 IsSemimoduleHomomorphism M₁ M₃ (g ∘ f)
253253 isSemimoduleHomomorphism f-homo g-homo = record
254254 { isBisemimoduleHomomorphism = isBisemimoduleHomomorphism ≈ᴹ₃-trans F.isBisemimoduleHomomorphism G.isBisemimoduleHomomorphism
255- } where module F = IsSemimoduleHomomorphism f-homo; module G = IsSemimoduleHomomorphism g-homo
255+ } where module F = IsSemimoduleHomomorphism M₁ M₂ f-homo; module G = IsSemimoduleHomomorphism M₂ M₃ g-homo
256256
257257 isSemimoduleMonomorphism : IsSemimoduleMonomorphism M₁ M₂ f →
258258 IsSemimoduleMonomorphism M₂ M₃ g →
259259 IsSemimoduleMonomorphism M₁ M₃ (g ∘ f)
260260 isSemimoduleMonomorphism f-mono g-mono = record
261261 { isSemimoduleHomomorphism = isSemimoduleHomomorphism F.isSemimoduleHomomorphism G.isSemimoduleHomomorphism
262262 ; injective = F.injective ∘ G.injective
263- } where module F = IsSemimoduleMonomorphism f-mono; module G = IsSemimoduleMonomorphism g-mono
263+ } where module F = IsSemimoduleMonomorphism M₁ M₂ f-mono; module G = IsSemimoduleMonomorphism M₂ M₃ g-mono
264264
265265 isSemimoduleIsomorphism : IsSemimoduleIsomorphism M₁ M₂ f →
266266 IsSemimoduleIsomorphism M₂ M₃ g →
267267 IsSemimoduleIsomorphism M₁ M₃ (g ∘ f)
268268 isSemimoduleIsomorphism f-iso g-iso = record
269269 { isSemimoduleMonomorphism = isSemimoduleMonomorphism F.isSemimoduleMonomorphism G.isSemimoduleMonomorphism
270270 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
271- } where module F = IsSemimoduleIsomorphism f-iso; module G = IsSemimoduleIsomorphism g-iso
271+ } where module F = IsSemimoduleIsomorphism M₁ M₂ f-iso; module G = IsSemimoduleIsomorphism M₂ M₃ g-iso
272272
273273module _
274274 {R : Set r}
@@ -286,20 +286,20 @@ module _
286286 IsModuleHomomorphism M₁ M₃ (g ∘ f)
287287 isModuleHomomorphism f-homo g-homo = record
288288 { isBimoduleHomomorphism = isBimoduleHomomorphism ≈ᴹ₃-trans F.isBimoduleHomomorphism G.isBimoduleHomomorphism
289- } where module F = IsModuleHomomorphism f-homo; module G = IsModuleHomomorphism g-homo
289+ } where module F = IsModuleHomomorphism M₁ M₂ f-homo; module G = IsModuleHomomorphism M₂ M₃ g-homo
290290
291291 isModuleMonomorphism : IsModuleMonomorphism M₁ M₂ f →
292292 IsModuleMonomorphism M₂ M₃ g →
293293 IsModuleMonomorphism M₁ M₃ (g ∘ f)
294294 isModuleMonomorphism f-mono g-mono = record
295295 { isModuleHomomorphism = isModuleHomomorphism F.isModuleHomomorphism G.isModuleHomomorphism
296296 ; injective = F.injective ∘ G.injective
297- } where module F = IsModuleMonomorphism f-mono; module G = IsModuleMonomorphism g-mono
297+ } where module F = IsModuleMonomorphism M₁ M₂ f-mono; module G = IsModuleMonomorphism M₂ M₃ g-mono
298298
299299 isModuleIsomorphism : IsModuleIsomorphism M₁ M₂ f →
300300 IsModuleIsomorphism M₂ M₃ g →
301301 IsModuleIsomorphism M₁ M₃ (g ∘ f)
302302 isModuleIsomorphism f-iso g-iso = record
303303 { isModuleMonomorphism = isModuleMonomorphism F.isModuleMonomorphism G.isModuleMonomorphism
304304 ; surjective = Func.surjective _ _ (_≈ᴹ_ M₃) F.surjective G.surjective
305- } where module F = IsModuleIsomorphism f-iso; module G = IsModuleIsomorphism g-iso
305+ } where module F = IsModuleIsomorphism M₁ M₂ f-iso; module G = IsModuleIsomorphism M₂ M₃ g-iso
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