Commutative diagram
In mathematics, especially the many applications of category theory, a commutative diagram is a diagram of objects and morphisms such that, when picking two objects, one can follow any path through the diagram and obtain the same result by composition.For example, the first isomorphism theorem is a commutative triangle as follows:
Since f = h o φ, the left diagram is commutative; and since φ = k o f, so is the right diagram.
Similarly, the square above is commutative if y o w = z o x.
Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative if every polygonal subdiagram is commutative.
That I, thy son, with foreign foemen's arms,
'Tis to reclaim my heritage I come,
Here the Varegers, my forefathers, ruled,
I am the last of all their lineage, snatched
The tocsin is heard. GLEB, ILIA, and TIMOSKA rush in,
Why are they running?
ILIA (entering from another house).
Neighbors, come forth! Come all, to council come!
[Enter OLEG and IGOR, with many other peasants,
Whence come ye hither with your wives and children?
IGOR.
At Maromesk, and slaughters all he finds.
OLEG.
We've fired our cottages, there's not a soul
Up country for the army.html">army of the Czar.
TIMOSKA.
enter on different sides.
IWANSKA.
How! What is this!
ILIA.
Who are you?
PETRUSCHKA.
What means all this? There a whole village.html">village flies
Make for the very point whence these have fled,
What foe? It is no foe that comes; it is
* * * * *
Vacillation of the inhabitants of the village between the two parties.
scale.
the Czar Boris conquers in a manner against its will, and does not follow
and is with difficulty prevented from doing so by Korela and Odowalsky.
Camp of the army of the CZAR BORIS. He is absent himself, and this
but not to be relied on. The leaders are not unanimous, and partly
number, Soltikow, declares for him from conviction. His adherence is
deserts to DEMETRIUS.
has faithful servants around him; but already he is discomposed by evil
rebellion in Moscow. He is also ashamed as Czar to enter the field in
.
On
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