Colibrì is a X-ray telescope which is currently in the concept study phase. The main objective of the Colibrì mission is to study the structure of accretion flows in the near vicinity of black holes and neutron stars and the study of emission from the surface of neutron stars. With high spectral and time resolution, and high throughput, Colibrì will allow the study of accretion disks and coronae, including reflection and re-emission of radiation by the disk, and observations of isolated and accreting neutron stars.The Colibrì concept is based on multiple non-imaging X-ray collectors similar to NICER but with cryogenically cooled transition edge (TES) detectors for high energy resolution and sensitivity. Colibrì aims to achieve an energy resolution finer than 1eV at 2keV (3eV at 6keV), and count rates up to 100kHz, in an energy range of 0.1-10keV. The timing precision of Colibrì aims to be better than 1 micro-sec, matching the innermost orbital period for a 10 solar-mass black hole. The total effective area of Colibrì is to be at least 2000 cm2 at 6.4keV. The study began in fall 2018 represented by multiple academic and industry partners encompassing a large portion of the Canadian high energy astronomy community. Continued mission development will increase Canadian capabilities in a number of facets. Highly qualified personnel (HQP) would be trained by via science and instrumentation studies. Moving towards mission flight also allows for the retention of HQP in astronomy, the space industry, and related fields within Canada. As Colibrì will take advantage of TES detector technology, the team is collaborating with the Stewart Blusson Quantum Matter Institute in order to develop and build the detectors at UBC, building Canadian technical capabilities to produce sensors which are widely used in industry and scientific experiments. The continued development of the Colibrì mission would lead to the first Canadian-led flagship X-ray telescope.