Operations on Module Maps
If module homomorphisms a
and b
with codomain(a) === domain(b)
are given, then compose(a, b)
refers to the composition b
$\circ$ a
. If an isomorphism of modules a
is given, then inv(a)
refers to its inverse.
hom_product
— Methodhom_product(M::ModuleFP, N::ModuleFP, A::Matrix{<:ModuleFPHom{<:ModuleFP, <:ModuleFP, Nothing}})
Given modules M
and N
which are products with r
respective s
factors, say $M = \prod_{i=1}^r M_i$, $N = \prod_{j=1}^s N_j$, and given a $r \times s$ matrix A
of homomorphisms $a_{ij} : M_i \to N_j$, return the homomorphism $M \to N$ with $ij$-components $a_{ij}$.
hom_tensor
— Methodhom_tensor(M::ModuleFP, N::ModuleFP, V::Vector{<:ModuleFPHom})
Given modules M
, N
which are tensor products with the same number of factors, say $M = M_1 \otimes \cdots \otimes M_r$, $N = N_1 \otimes \cdots \otimes N_r$, and given a vector V
of homomorphisms $a_i : M_i \to N_i$, return $a_1 \otimes \cdots \otimes a_r$.
lift_homomorphism_contravariant
— Methodlift_homomorphism_contravariant(Hom_MP::ModuleFP, Hom_NP::ModuleFP, a::ModuleFPHom)
Given modules of homomorphism, say, Hom_MP
$= \text{Hom}(M,P)$ and Hom_NP
$= \text{Hom}(N,P)$, and given a homomorphism a
$: N \to M$, return the induced homomorphism $\text{Hom}(M,P) \to \text{Hom}(N,P)$.
lift_homomorphism_covariant
— Methodlift_homomorphism_covariant(Hom_PM::ModuleFP, Hom_PN::ModuleFP, a::ModuleFPHom)
Given modules of homomorphism, say, Hom_PM
$= \text{Hom}(P,M)$ and Hom_PN
$= \text{Hom}(P,N)$, and given a homomorphism a
$: M \to N$, return the induced homomorphism $\text{Hom}(P,M) \to \text{Hom}(P,N)$.