 Construction of small limits from products and equalizers

ID: construction-of-small-limits-from-products-and-equalizers

If all small products and equalizers exist, the limit of

D : J \to C

is the equalizer of the two maps

\prod_{j \in J} D (j) ⇉ \prod_{u : i \to j} D (j),

whose

u

-coordinates are respectively

D (u)

after projection to

D (i)

and direct projection to

D (j)

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