Nuprl Definition : is-short-exact

is-short-exact(A;B;C;f;g) ==
  (∀a:Point(A). (a ∈ Ker(f) ⇐⇒ a = 0 ∈ Point(A)))
  ∧ (∀b:Point(B). (b ∈ Img(f) ⇐⇒ b ∈ Ker(g)))
  ∧ (∀c:Point(C). c ∈ Img(g))

Definitions occuring in Statement : vs-map-image: b ∈ Img(f), vs-map-kernel: a ∈ Ker(f), vs-0: 0, vs-point: Point(vs), all: ∀x:A. B[x], iff: P ⇐⇒ Q, and: P ∧ Q, equal: s = t ∈ T
Definitions occuring in definition : equal: s = t ∈ T, vs-0: 0, and: P ∧ Q, iff: P ⇐⇒ Q, vs-map-kernel: a ∈ Ker(f), all: ∀x:A. B[x], vs-point: Point(vs), vs-map-image: b ∈ Img(f)
FDL editor aliases : is-short-exact

Latex:
is-short-exact(A;B;C;f;g) == (\mforall{}a:Point(A). (a \mmember{} Ker(f) \mLeftarrow{}{}\mRightarrow{} a = 0)) \mwedge{} (\mforall{}b:Point(B). (b \mmember{} Img(f) \mLeftarrow{}{}\mRightarrow{} b \mmember{} Ker(g))) \mwedge{} (\mforall{}c:Point(C). c \mmember{} Img(g)) Date html generated: 2019_10_31-AM-06_27_37 Last ObjectModification: 2019_08_21-PM-06_28_12 Theory : linear!algebra Home Index