A functor between two categories is termed product-preserving if it ... Suppose \mathcal{C},\mathcal{D} are categories. A functor \mathcal{F}: ... ...
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An equivalence of categories is a functor between two categories that satisfies the following three conditions:
* It is full: It is surjective ... ...
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A functor between two categories is termed pullback-preserving if it maps any pullback diagram in the first category to a pullback diagram in ... ...
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\to \mathcal{D} is a functor between two categories. We say that \mathcal{F} is faithful if it is true that for any objects A,B \in \mathcal{C} ... ...
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\to \mathcal{D} is a functor between two categories. We say that \mathcal{F} is conservative if, whenever A,B \in \operatorname{Ob} \mathcal{C} ... ...
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\to \mathcal{D} is a functor between two categories. \mathcal{F} is termed full if for any A,B \in \operatorname{Ob}\mathcal{C}, the induced ... ...
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