Could debt cause inflation instead of deflation? It is well known that debt can cause deflation, especially during crisis: to repay their debts agents sell their goods which causes a fall in prices.

But if there is no crisis and agents "have the time" to repay their debt, would it be possible to have the opposite mechanism, inflation: to repay their debts (and make their investments profitable) agents would sell their products for an higher price causing a raise in prices?

In the general case it seems difficult because this could destroy market shares if there is competition.

But in some cases I wonder if it could:


monopolys (especially state monopolys, and this would be a kind of hidden tax),
competition but with all competitors in debt so that all have to sell at higher prices to survive,
...
Yes it can.

If debt originates from the banking system, then it potentially has a side effect of money creation. Whether or not money is actually created when a bank loan is made depends on the banking system's regulatory framework, and the lending policies of its banks, and these can vary widely. 

However if there is net excess of bank lending over bank loan repayment and loan default, then money creation is occurring, and the additional money can and indeed usually does, result in inflation.