| 单词 | covariant functor |
| 释义 | > as lemmascovariant functor Functors are typically classified as either covariant or contravariant. The criteria for a mapping F between two categories to be a covariant functor are that: if f: X → Y is a morphism in the first category, then F( f ) is a morphism from F( X ) to F( Y ); the identity morphism of the first category is mapped to that of the second; and the mapping preserves composition of morphisms. Using the same notation as above, the criteria for a mapping to be a contravariant functor is almost identical, the only differences being that F ( f ) is a morphism from F( Y ) to F ( X ), and the order of composition of morphisms is reversed—e.g. if ∘ represents the operation of composition, then F( f∘g) = F( g )∘F( f ).extracted from functorn.< as lemmas |
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