SELECT 
  pc.category_id, 
  COUNT(pc.product_id) AS products_count 
FROM 
  cscart_products_categories AS pc 
  LEFT JOIN cscart_products AS p ON p.product_id = pc.product_id 
  LEFT JOIN cscart_companies AS c ON p.company_id = c.company_id 
WHERE 
  p.status = 'A' 
  AND p.paused = 'N' 
  AND c.status = 'A' 
  AND (
    p.amount >= p.min_qty 
    OR (
      p.min_qty IS NULL 
      AND p.amount > 0
    )
  ) 
  AND pc.category_id IN (
    105, 106, 107, 108, 109, 110, 111, 112
  ) 
GROUP BY 
  pc.category_id

Query time 0.00108

Result

category_id products_count
105 14
106 1
107 1
108 1
109 1
110 1
111 1
112 1