fix some typos

docs/src/quad_forms/lattices.md

@@ -257,9 +257,9 @@ pseudo_matrix(Lquad)
 ```
 
 ## Categorical constructions
-Given a finite collection of lattices, one can construct their direct sums, which
+Given finite collections of lattices, one can construct their direct sums, which
 are also direct products in this context. They are also sometimes called biproducts.
-Depending on the user usage, it is possible to call one of the following function.
+Depending on the user usage, it is possible to call one of the following functions.
 
 ```@docs
 direct_sum(x::Vector{AbstractLat})

src/GrpAb/GrpAbFinGen.jl

@@ -597,7 +597,7 @@ with the injections $G_i \to D$.
 
 For finite abelian groups, finite direct sums and finite direct products agree and
 they are therefore called biproducts.
-If one wants to obtain $D$ as a direct_product together with the projections
+If one wants to obtain $D$ as a direct product together with the projections
 $ D \to G_i$, one should call `direct_product(G...)`.
 If one wants to obtain $D$ as a biproduct together with the projections and the
 injections, one should call `biproduct(G...)`.

src/QuadForm/Lattices.jl

@@ -1494,10 +1494,9 @@ end
     direct_sum(x::Vararg{T}) where T <: AbstractLat -> T, Vector{AbstractSpaceMor}
     direct_sum(x::Vector{T}) where T <: AbstractLat -> T, Vector{AbstractSpaceMor}
 
-Given a collection of quadratic or hermitian lattices
-$\mathbb Z$-lattices $L_1, \ldots, L_n$, return their direct sum
-$L := L_1 \oplus \ldots \oplus L_n$, together with the injections $L_i \to L$
-(seen as maps between the corresponding ambient spaces).
+Given a collection of quadratic or hermitian lattices $L_1, \ldots, L_n$,
+return their direct sum $L := L_1 \oplus \ldots \oplus L_n$, together with
+the injections $L_i \to L$ (seen as maps between the corresponding ambient spaces).
 
 For objects of type `AbstractLat`, finite direct sums and finite direct
 products agree and they are therefore called biproducts.
@@ -1519,10 +1518,9 @@ direct_sum(x::Vararg{AbstractLat}) = direct_sum(collect(x))
     direct_product(x::Vararg{T}) where T <: AbstractLat -> T, Vector{AbstractSpaceMor}
     direct_product(x::Vector{T}) where T <: AbstractLat -> T, Vector{AbstractSpaceMor}
 
-Given a collection of quadratic or hermitian lattices
-$\mathbb Z$-lattices $L_1, \ldots, L_n$, return their direct product
-$L := L_1 \times \ldots \times L_n$, together with the projections $L \to L_i$
-(seen as maps between the corresponding ambient spaces).
+Given a collection of quadratic or hermitian lattices $L_1, \ldots, L_n$,
+return their direct product $L := L_1 \times \ldots \times L_n$, together with
+the projections $L \to L_i$ (seen as maps between the corresponding ambient spaces).
 
 For objects of type `AbstractLat`, finite direct sums and finite direct
 products agree and they are therefore called biproducts.
@@ -1544,10 +1542,10 @@ direct_product(x::Vararg{AbstractLat}) = direct_product(collect(x))
     biproduct(x::Vararg{T}) where T <: AbstractLat -> T, Vector{AbstractSpaceMor}, Vector{AbstractSpaceMor}
     biproduct(x::Vector{T}) where T <: AbstractLat -> T, Vector{AbstractSpaceMor}, Vector{AbstractSpaceMor}
 
-Given a collection of quadratic or hermitian lattices
-$\mathbb Z$-lattices $L_1, \ldots, L_n$, return their biproduct
-$L := L_1 \oplus \ldots \oplus L_n$, together with the injections $L_i \toL$
-and the projections $L \to L_i$ (seen as maps between the corresponding ambient spaces).
+Given a collection of quadratic or hermitian lattices $L_1, \ldots, L_n$,
+return their biproduct $L := L_1 \oplus \ldots \oplus L_n$, together with
+the injections $L_i \toL$ and the projections $L \to L_i$ (seen as maps
+between the corresponding ambient spaces).
 
 For objects of type `AbstractLat`, finite direct sums and finite direct
 products agree and they are therefore called biproducts.