Difference between revisions of "SFN:Math-test"
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{{defn|name=Definition 1|note=Definition of set-based categories|label=df:sbcat | {{defn|name=Definition 1|note=Definition of set-based categories|label=df:sbcat | ||
|Let $\cc$ be a small category and let $U:\cc\to\set$ be a functor. We | |Let $\cc$ be a small category and let $U:\cc\to\set$ be a functor. We | ||
| − | say that $\cc$ is ''set-based'' (\sbcat | + | say that $\cc$ is ''set-based'' ($\sbcat$ for short) with respect |
to $U$ if the pair $(\cc,U)$ satisfy the following: | to $U$ if the pair $(\cc,U)$ satisfy the following: | ||
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Revision as of 05:33, 29 March 2014
$ \newcommand\cc{\mathcal{C}} \newcommand\set{\mathsf{Set}} \newcommand\sbcat{\ensuremath{\mathit{Category}}}
$
Definition 1 (Definition of set-based categories)
Let $\cc$ be a small category and let $U:\cc\to\set$ be a functor. We
say that $\cc$ is set-based ($\sbcat$ for short) with respect to $U$ if the pair $(\cc,U)$ satisfy the following:
Notice that the condition (Sb:b) implies that the functor $U$ preserves image--factorizations: