Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

A-Adjoint Functors

We now run through the sorites related to adjointness of A-functors. Later, we will be constructing numerous functorial maps between multivariate A-functors by purely formal (category-theoretic) methods. The results in this section, together with the Proposition in 1.5, will guarantee that the so-constructed maps are in fact A-functorial. [Pg.97]

When these conditions hold, we say that f, 0 ) and (/, 0 ) are A-adjoint, or—leaving 6 and 0 to the readet—that (/, / ) is a A-adjoint pair. [Pg.97]

Proof (i) = (ii). Chase a map f A B around the diagram in both directions to reduce to showing that the following diagram commutes  [Pg.97]

Example 3.3.2. Quasi-inverse A-equivalences of categories (1.7.2) are A-adjoint pairs. [Pg.98]

Then this pair (/, / ) is A-adjoint. To verify condition (ii) in (3.3.1), consider the following diagram of natural isomorphisms, where H stands for RHom and T L stands for RWom  [Pg.98]


See other pages where A-Adjoint Functors is mentioned: [Pg.97]    [Pg.97]    [Pg.99]   


SEARCH



Adjoint

Adjoints

Functor

© 2024 chempedia.info