Search Results for ""

A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f ...

A diagram lemma which states that the above commutative diagram of Abelian groups and group homomorphisms with exact rows gives rise to an exact sequence This commutative ...

A diagram lemma which states that every short exact sequence of chain complexes and chain homomorphisms 0-->C-->^phiD-->^psiE-->0 gives rise to a long exact sequence in ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

If, in the above commutative diagram of modules and module homomorphisms the columns and two upper rows are exact, then so is the bottom row.

A type of diagram invented by Lewis Carroll (the name is an abbreviation of "Lewis") that can be used to determine the number of minimal covers of n numbers with k members.

A partition p is said to contain another partition q if the Ferrers diagram of p contains the Ferrers diagram of q. For example, {3,3,2} (left figure) contains both {3,3,1} ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

A semi-oriented 2-variable knot polynomial defined by F_L(a,z)=a^(-w(L))<|L|>, (1) where L is an oriented link diagram, w(L) is the writhe of L, |L| is the unoriented diagram ...

In category theory, a tensor category (C, tensor ,I,a,r,l) consists of a category C, an object I of C, a functor tensor :C×C->C, and a natural isomorphism a = a_(UVW):(U ...