are Derby Cathedral and  Carlisle Cathedral in the same country
yes
Title: Derby Cathedral
Passage: Derby Cathedral, known as the Cathedral of All Saints, is a grade I listed cathedral church in the city of Derby, in the county of Derbyshire, England.  It was promoted from parish church status into a cathedral in 1927 in order to create a seat for the Bishop of Derby, which new see was created in that year.  The original church of All Saints was founded in the mid-10th century as a royal collegiate church, dedicated to All Saints.  It became a cathedral in 1927.  The main body of the church as it stands today is a Georgian rebuilding by James Gibbs, completed in 1725.  The tower dates from the 16th century, and a retrochoir was added in the 20th century.
Title: Carlisle Cathedral
Passage: The Cathedral Church of the Holy and Undivided Trinity, otherwise called Carlisle Cathedral, is the seat of the Anglican Bishop of Carlisle.  It is located in Carlisle, in Cumbria, North West England.  It was founded as an Augustinian priory and became a cathedral in 1133.
Title: Diocese of Derby
Passage: The Diocese of Derby is a Church of England diocese in the Province of Canterbury, roughly covering the same area as the County of Derbyshire.  Its diocesan bishop is the Bishop of Derby who has his seat at Derby Cathedral.  The diocesan bishop is assisted by the suffragan bishop, the bishop of Repton.
Derby Cathedral Carlisle Cathedral