def counit(A):
assert isinstance(A, Cell1)
src = A * A.dual
tgt = Cell1.identity(A.tgt)
assert tgt.hom == src.hom
shape = tgt.shape
n = shape[0]
assert n == shape[1]
rig = A.rig
ring = rig.ring
linss = []
for i in range(n):
lins = [] # row
for k in range(n):
t, s = tgt[i, k], src[i, k]
if i != k:
lin = Lin.zero(t, s)
else:
# argh... why can't we direct_sum the Lin.counit's ?
a = elim.zeros(ring, t.n, s.n)
idx = 0
for j in range(A.shape[1]):
counit = Lin.counit(rig.one, A[i, j])
a[:, idx:idx + counit.shape[1]] = counit.A
idx += counit.shape[1]
assert idx == s.n
lin = Lin(t, s, a)
lins.append(lin)
linss.append(lins)
return Cell2(tgt, src, linss)
def zero(cls, tgt, src): # tgt <---- src
assert isinstance(tgt, Cell1)
assert isinstance(src, Cell1)
assert tgt.rig == src.rig
assert tgt.hom == src.hom
rig = tgt.rig
rows, cols = tgt.shape
linss = [[Lin.zero(tgt[i, j], src[i, j]) for j in range(cols)]
for i in range(rows)]
return Cell2(tgt, src, linss)