In category theory in mathematics, a coherent category is a regular category in which the poset of subobjects S u b ( X ) {\displaystyle \mathrm {Sub} (X)} has finte unions and each f ∗ : S u b ( B ) → S u b ( A ) {\displaystyle f^{*}:\mathrm {Sub} (B)\rightarrow \mathrm {Sub} (A)} perserves them. Makkai & Reyes (1977) called logical categories, and according to Makkai & Reyes (1977), the coherent category was introduced by Joyal and Gonzalo E. Reyes.
In category theory in mathematics, a coherent category is a regular category in which the poset of subobjects S u b ( X ) {\displaystyle \mathrm {Sub} (X)} has finte unions and each f ∗ : S u b ( B ) → S u b ( A ) {\displaystyle f^{*}:\mathrm {Sub} (B)\rightarrow \mathrm {Sub} (A)} perserves them. Makkai & Reyes (1977) called logical categories, and according to Makkai & Reyes (1977), the coherent category was introduced by Joyal and Gonzalo E. Reyes.
Source: Wikipedia "Coherent category" · CC BY-SA 4.0
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