nLab regular and exact categories - contents

∞-ary regular and exact categories

• exactness property

• arity class: unary, finitary, infinitary

regularity

• regular category = unary regular

• coherent category = finitary regular

  • Heyting category/logos = finitary regular + universal quantifier

• geometric category = infinitary regular

exactness

• exact category = unary exact

• pretopos = finitary exact = exact + extensive