3 papers
math.RT2025
On preservation of relative resolutions for poset representations
Toshitaka Aoki, Shunsuke Tada
The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the ad…
math.AT2024
Bipath Persistence
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this se…
math.RT2023
Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
Recently, there is growing interest in the use of relative homology algebra to develop invariants using interval covers and interval resolutions (i.e., right minimal approximations…